Year: 2013
Type: preprint
Abstract: A map $f:X\to Y$ to a simplicial complex $Y$ is called a $Y$-triangular homotopy equivalence if it has a homotopy inverse $g$ and homotopies $h_1:f\circ g\simeq \mathrm{id}_Y$, $h_2:g\circ f\simeq \mathrm{id}_X$ such that for all simplices $σ\in Y$, $f|_σ:f^{-1}(σ) \to σ$ is a homotopy equivalence with inverse $g|_σ:σ\to f^{-1}(σ)$ and homotopies $h_1|_σ$ and $h_2|_σ$. In this paper we prove that for all pairs $X,Y$ of finite-dimensional locally finite simplicial complexes there is an $ε(X,Y)>0$ such that any $ε$-controlled homotopy equivalence $f:X\to Y$ for $ε0$.
Source: arXiv (Cornell University)
Author: Adams-Florou, Spiros
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W258748738