Contact spectral invariants and persistence

2015/02/20 by Maia Fraser, Fraser, Maia
Computer Science · Mathematics · #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1502.05979

openalex publication_date 2015/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This sketch shows that the usual generating function based capacities have an interpretation in the language of persistent homology as persistences of certain homology classes in the persistence module formed by the corresponding generating function homology groups. This viewpoint suggests various new invariants, in particular a ℤ_k-equivariant capacity which can be used to prove orderability of lens spaces, proved by Milin (2008) using contact homology and by Sandon (2010) using equivariant generating function homology. These are informal notes originally circulated in January 2014.

Citations

• Persistent Homology of Filtered Covers

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