Simple homotopy theory and nerve theorem for categories

DOI10.1016/j.topol.2021.107609zbMath1461.55013OpenAlexW3123086240MaRDI QIDQ1998811

Kohei Tanaka

Publication date: 9 March 2021

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2021.107609

zbMATH Keywords

posetsimplicial complexsmall categorynerve theoremsimple homotopy\(\Delta\)-complex

Mathematics Subject Classification ID

Partial orders, general (06A06) Persistent homology and applications, topological data analysis (55N31) Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. (57Q10) Abstract complexes in algebraic topology (55U05) Combinatorial aspects of simplicial complexes (05E45) Group actions on combinatorial structures (05E18) Discrete Morse theory and related ideas in manifold topology (57Q70)

Related Items

Good covers for vortex nerve cell complexes. free group presentation of intersecting nested cycles in planar CW spaces, Good coverings of proximal Alexandrov spaces. Path cycles in the extension of the Mitsuishi-Yamaguchi good covering and Jordan Curve Theorems, Cone complexes and group actions

Uses Software

• Perseus

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Morse theory for filtrations and efficient computation of persistent homology
• On Quillen's theorem A for posets
• Strong homotopy types, nerves and collapses
• On the subdivision of small categories
• Extensions of complexes of groups
• Topological hypercovers and \(\mathbb{A}^1\)-realizations
• Čech complexes for covers of small categories
• Computing persistent homology
• Categories and cohomology theories
• Topological persistence and simplification
• The cylinder of a relation and generalized versions of the nerve theorem
• The homotopy type of the Baily-Borel and allied compactifications
• Categories and orbispaces
• Geometric topology. Localization, periodicity and Galois symmetry. The 1970 MIT Notes. Edited by A. Ranicki
• Strong homotopy types of acyclic categories and \(\varDelta\)-complexes
• Simple homotopy types and finite spaces
• Classifying spaces and spectral sequences
• Semi-simplicial complexes and singular homology
• A model structure on the category of small categories for coverings
• Topology and data
• Higher algebraic K-theory: I
• Finite Topological Spaces
• Homotopy Type Comparison of a Space with Complexes Associated with its Open Covers
• On a Conjecture of Andre Weil
• Δ-SETS I: HOMOTOPY THEORY
• On the imbedding of systems of compacta in simplicial complexes
• Simple Homotopy Types
• Combinatorial algebraic topology