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arxiv: math/9911159 · v1 · submitted 1999-11-21 · 🧮 math.GT · math.QA

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String Topology

Moira Chas , Dennis Sullivan
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classification 🧮 math.GT math.QA
keywords familycurvearoundclosedgoingbehindconsidercurves
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Consider two families of closed oriented curves in a d-manifold. At each point of intersecction of a curve of one family with a curve of the other family, form a new closed curve by going around the first curve and then going around the second. Typically, an i-dimensional family and a j-dimensional family will produce an (i+j-d+2)-dimensional family. Our purpose is to describe mathematical structure behind such interactions.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. On the growth rate of Reeb orbit on star-shaped hypersurfaces

    math.SG 2026-05 unverdicted novelty 6.0

    Under a non-nilpotency condition in free loop space homology with respect to the Chas-Sullivan product, the number of simple Reeb orbits on star-shaped hypersurfaces grows at least like T/log(T).