Combinatorial models for topological Reeb spaces

Paul Trygsland

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arXiv · 2109.05474

Combinatorial models for topological Reeb spaces

Paul Trygsland

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Abstract

There are two rather distinct approaches to Morse theory nowadays: smooth and discrete. We propose to study a real valued function by assembling all associated sections in a topological category. From this point of view, Reeb functions on stratified spaces are introduced, including both smooth and combinatorial examples. As a consequence of the simplicial approach taken, the theory comes with a spectral sequence for computing (generalized) homology. We also model the homotopy type of Reeb graphs/ topological Reeb spaces as simplicial sets, which are combinatorial in nature, as opposed to the typical description in terms of quotient spaces.

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Paul Trygsland. 2021-09-12. Combinatorial models for topological Reeb spaces. https://arxiv.org/abs/2109.05474

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