Constructs closed aspherical 4-manifolds that are homeomorphic but not diffeomorphic, providing counterexamples to the smooth Borel conjecture in dimension 4.
Gompf and Andr\' a s I
9 Pith papers cite this work. Polarity classification is still indexing.
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Constructs non-split 2-component links in S^4 to obtain topologically split but smoothly non-split links in #^n CP^2, yielding exotic simply connected definite 4-manifolds with boundary and exotic Mazur manifold embeddings in S^4.
Mazur and Jester manifolds have pairwise nonhomeomorphic boundaries via an octahedral hyperbolic structure, Dehn filling, and systolic geodesics, distinguishing their contractible 4-manifolds.
Singular instanton Floer homology produces exotic pairs of slice disks for a strongly invertible Z-slice knot whose symmetric disks stay exotic under stabilizations by definite 4-manifolds or projective planes.
A new framework classifies PL-types for every triangulated 4-manifold with up to six pentachora, succeeding except on the 4-sphere, CP^2 and QS^4(2) where at most four, three and two types appear respectively.
Computes symmetric ribbon numbers r_s(K) for knots of crossing number ≤12 and supplies polynomial lower bounds.
Gives an explicit method to build (12n-2,0)-trisection diagrams for E(n) from Lefschetz fibration handle diagrams.
Knot traces of alternating knots and the newly defined extended alternating knots admit PALFs whose regular fibers have genus equal to the number of white regions in their planar graphs.
A combinatorial extension of a PALF construction produces genus-1 fiber versions on knot traces of Legendrian positive twist knots and positive torus knots T_{2,2n+1} while preserving the diffeomorphism type of the total space.
citing papers explorer
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Exotic aspherical 4-manifolds
Constructs closed aspherical 4-manifolds that are homeomorphic but not diffeomorphic, providing counterexamples to the smooth Borel conjecture in dimension 4.
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Links of Mazur manifolds and exotica
Constructs non-split 2-component links in S^4 to obtain topologically split but smoothly non-split links in #^n CP^2, yielding exotic simply connected definite 4-manifolds with boundary and exotic Mazur manifold embeddings in S^4.
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Mazur's knot and the Octahedron
Mazur and Jester manifolds have pairwise nonhomeomorphic boundaries via an octahedral hyperbolic structure, Dehn filling, and systolic geodesics, distinguishing their contractible 4-manifolds.
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Exotic disks and singular instanton Floer homology
Singular instanton Floer homology produces exotic pairs of slice disks for a strongly invertible Z-slice knot whose symmetric disks stay exotic under stabilizations by definite 4-manifolds or projective planes.
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Small Triangulations of $4$-Manifolds: Introducing the $4$-Manifold Census
A new framework classifies PL-types for every triangulated 4-manifold with up to six pentachora, succeeding except on the 4-sphere, CP^2 and QS^4(2) where at most four, three and two types appear respectively.
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Symmetric ribbon numbers of low-complexity knots
Computes symmetric ribbon numbers r_s(K) for knots of crossing number ≤12 and supplies polynomial lower bounds.
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Minimal genus trisection diagrams of the elliptic surfaces $E(n)$ via handle diagrams
Gives an explicit method to build (12n-2,0)-trisection diagrams for E(n) from Lefschetz fibration handle diagrams.
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Lefschetz Fibrations on Knot Traces of Alternating and Extended Alternating Knots
Knot traces of alternating knots and the newly defined extended alternating knots admit PALFs whose regular fibers have genus equal to the number of white regions in their planar graphs.
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Combinatorial extension of a simple construction of Lefschetz fibrations
A combinatorial extension of a PALF construction produces genus-1 fiber versions on knot traces of Legendrian positive twist knots and positive torus knots T_{2,2n+1} while preserving the diffeomorphism type of the total space.