Paper Citation Record · LEDGER

Fundamental examples of height functions on closed manifolds and their 1st derivatives

As of 17 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 0 inbound Pith citation observations for arXiv:2608.00556.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2608.00556 v1

Coverage vector

measured 49 of 49 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-05T00:54:17.047306Z

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Pith citing papers itemized under the disclosed page cap.

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Reference resolution

49 of 49 outbound references displayed

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Outbound references

Observation e8584070-7ed4-4784-9972-5c83fedde0f0 · outbound

This paper cites Banyaga and D.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Banyaga and D

Reference 1

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This paper cites Banchoﬀ and F.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Banchoﬀ and F

Reference 2

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Observation 0147e878-477c-4ca4-83a2-760e1a53c07f · outbound

This paper cites Burlet and V.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Burlet and V

Reference 3

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Observation b79e3abb-cee9-4bb6-82c2-a7293056e89f · outbound

This paper cites Bott, Nondegenerate critical manifolds , Ann.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Bott, Nondegenerate critical manifolds , Ann

Reference 4

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Reference 5

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This paper cites Burlet and G.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Burlet and G

Reference 6

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Reference 7

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Observation 43fbbb40-07ea-42d4-8b33-2ff92042d557 · outbound

This paper cites Gelbukh, A ﬁnite graph is homeomorphic to the Reeb graph of a Morse-Bot t function , Mathematica Slovaca, 71 (3), 757–772, 2021; doi: 10.1515/m s-2021-0018.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Gelbukh, A ﬁnite graph is homeomorphic to the Reeb graph of a Morse-Bot t function , Mathematica Slovaca, 71 (3), 757–772, 2021; doi: 10.1515/m s-2021-0018

Reference 8

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Observation a4ed3d6c-44ce-487f-87f4-ac9242d20a1a · outbound

This paper cites Gelbukh, Morse-Bott functions with two critical values on a surface , Czechoslovak Mathe- matical Journal, 71 (3), 865–880, 2021; doi: 10.21136/CMJ.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Gelbukh, Morse-Bott functions with two critical values on a surface , Czechoslovak Mathe- matical Journal, 71 (3), 865–880, 2021; doi: 10.21136/CMJ

Reference 9

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Observation 963b031d-7408-44aa-8790-ad88b791b275 · outbound

This paper cites Gelbukh, Realization of a graph as the Reeb graph of a height function o n an embedded surface, Topol.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Gelbukh, Realization of a graph as the Reeb graph of a height function o n an embedded surface, Topol

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T00:54:17.821315Z

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Observation 69a85b87-1620-4d8b-95af-2a6d4a6d1e7d · outbound

This paper cites Gelbukh, On the topology of the Reeb graph , Publicationes Mathematicae Debrecen 104(3–.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Gelbukh, On the topology of the Reeb graph , Publicationes Mathematicae Debrecen 104(3–

Reference 11

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Observation e2251e1b-0f81-4bbb-a04a-e2db61f16658 · outbound

This paper cites Gelbukh, Realization of a digraph as the Reeb graph of a Morse-Bott fun ction on a given surface, Topology and its Applications, 2024.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Gelbukh, Realization of a digraph as the Reeb graph of a Morse-Bott fun ction on a given surface, Topology and its Applications, 2024

Reference 12

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Observation 563387ff-6070-4d5f-bbd6-479d755ea6ea · outbound

This paper cites Gelbukh, Reeb Graphs of Morse-Bott Functions on a Given Surface , Bulletin of the Iranian Mathematical Society, Volume 50 Article number 84, 2024, 1– 17.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Gelbukh, Reeb Graphs of Morse-Bott Functions on a Given Surface , Bulletin of the Iranian Mathematical Society, Volume 50 Article number 84, 2024, 1– 17

Reference 13

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Reference 14

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Observation 82605845-16aa-4db4-89b9-d5527f3f0c37 · outbound

This paper cites Golubitsky and V.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Golubitsky and V

Reference 15

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Reference 16

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Observation 25dea9b2-7d08-407b-baa3-58ab36094df2 · outbound

This paper cites On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values.

Fundamental examples of height functions on closed manifolds and their 1st derivatives On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values

Reference 17

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Observation d4a3b6e0-0d81-40bf-ae2f-ad35a2329ec2 · outbound

This paper cites On Reeb graphs induced from smooth functions on closed or open manifolds.

Fundamental examples of height functions on closed manifolds and their 1st derivatives On Reeb graphs induced from smooth functions on closed or open manifolds

Reference 18

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Observation 0f8ead0f-b7bb-4df8-a540-ae1b4d4afbb4 · outbound

This paper cites Real algebraic functions on closed manifolds whose Reeb spaces are given graphs.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Real algebraic functions on closed manifolds whose Reeb spaces are given graphs

Reference 19

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Observation e167c158-d63a-4da3-8877-28e5efa14e5a · outbound

This paper cites Realization problems of graphs as Reeb graphs of Morse functions with prescribed preimages.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Realization problems of graphs as Reeb graphs of Morse functions with prescribed preimages

Reference 20

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This paper cites Reconstructing real algebraic maps locally like moment-maps with prescribed images and compositions with the canonical projections to the $1$-dimensional real affine space.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Reconstructing real algebraic maps locally like moment-maps with prescribed images and compositions with the canonical projections to the $1$-dimensional real affine space

Reference 21

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Observation 40703d07-9ce5-4642-bacf-c546e69c5d52 · outbound

This paper cites Some remark on real algebraic maps which are topologically special generic maps and generalize the canonical projections of the unit spheres.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Some remark on real algebraic maps which are topologically special generic maps and generalize the canonical projections of the unit spheres

Reference 22

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Reference 23

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Observation 3fb814f6-cb3f-411c-9291-d460e7c39494 · outbound

This paper cites Kitazawa, Fundamental examples of Reeb spaces of smooth functions deﬁ ned from two graphs of smooth functions with same asymptotic behaviors , arXiv:2602.17014, 2026/2.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Kitazawa, Fundamental examples of Reeb spaces of smooth functions deﬁ ned from two graphs of smooth functions with same asymptotic behaviors , arXiv:2602.17014, 2026/2

Reference 24

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This paper cites Regions represented as foliated forms and natural smooth maps onto them.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Regions represented as foliated forms and natural smooth maps onto them

Reference 25

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Observation c14033b5-e6dd-4074-8dae-9c2f6d178c22 · outbound

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Reference 26

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Observation 202d5e83-e071-4a28-a670-28eab3a446c7 · outbound

This paper cites Martinez-Alfaro, I.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Martinez-Alfaro, I

Reference 27

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Fundamental examples of height functions on closed manifolds and their 1st derivatives Masumoto and O

Reference 28

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Fundamental examples of height functions on closed manifolds and their 1st derivatives N Mather, Stability of C∞ mappings

Reference 29

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Reference 30

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Reference 31

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Reference 34

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Reference 35

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Observation f6080977-5c33-4fe4-b0a8-b3495cc054c6 · outbound

This paper cites Mather, Notes on topological stability , Bull.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Mather, Notes on topological stability , Bull

Reference 36

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Observation 719236fb-8068-4ec7-86be-65597ec51c18 · outbound

This paper cites Realization of a graph as the Reeb graph of a Morse function on a manifold.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Realization of a graph as the Reeb graph of a Morse function on a manifold

Reference 37

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This paper cites Milnor, Morse Theory , Annals of Mathematic Studies AM-51, Princeton University Press; 1st Edition (1963.5.1).

Fundamental examples of height functions on closed manifolds and their 1st derivatives Milnor, Morse Theory , Annals of Mathematic Studies AM-51, Princeton University Press; 1st Edition (1963.5.1)

Reference 38

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Observation 8f2c1365-65b5-4431-b5fc-74e069db44c5 · outbound

This paper cites Milnor, Lectures on the h-cobordism theorem , Math.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Milnor, Lectures on the h-cobordism theorem , Math

Reference 39

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Observation c8932ef7-b193-4fee-8297-12fefe3896aa · outbound

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Fundamental examples of height functions on closed manifolds and their 1st derivatives Morishita and O

Reference 40

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Reference 41

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Observation 4e420f73-c8ba-47b4-8b0a-e2c9aa22c61b · outbound

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Fundamental examples of height functions on closed manifolds and their 1st derivatives Saeki, Notes on the topology of folds , J

Reference 42

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Fundamental examples of height functions on closed manifolds and their 1st derivatives Saeki, Topology of special generic maps of manifolds into Euclidea n spaces, Topology Appl

Reference 43

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Observation c9482f1b-ed65-4c49-848b-5146fcad1bb3 · outbound

This paper cites Saeki, Topology of singular ﬁbers of diﬀerentiable maps , Lecture Notes in Math., Vol.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Saeki, Topology of singular ﬁbers of diﬀerentiable maps , Lecture Notes in Math., Vol

Reference 44

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Reference 45

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Observation a7c7dd44-499a-441e-9014-8c9191a96e44 · outbound

This paper cites Saeki, Reeb spaces of smooth functions on manifolds II , Res.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Saeki, Reeb spaces of smooth functions on manifolds II , Res

Reference 46

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Observation 9fbb6d04-a343-413d-b967-69b9c20dd7eb · outbound

This paper cites Sharko, About Kronrod-Reeb graph of a function on a manifold , Methods of Functional Analysis and Topology 12 (2006), 389–396.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Sharko, About Kronrod-Reeb graph of a function on a manifold , Methods of Functional Analysis and Topology 12 (2006), 389–396

Reference 47

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Observation 27f67d91-8329-41aa-b1e3-13ad555b6f8e · outbound

This paper cites Thom, Les singularites des applications diﬀerentiables , Ann.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Thom, Les singularites des applications diﬀerentiables , Ann

Reference 48

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Observation 1ad9c0c5-39f0-49a3-8baf-5546be47fc18 · outbound

This paper cites Whitney, On singularities of mappings of Euclidean spaces: I, mappin gs of the plane into the plane , Ann.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Whitney, On singularities of mappings of Euclidean spaces: I, mappin gs of the plane into the plane , Ann

Reference 49

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