The double of a simplicial complex
Kathryn Lesh, Bridget Schreiner, Nathalie Wahl
TL;DR
This paper introduces the concepts of doubling and r-tupling for simplicial complexes, establishing connectivity results and linking r-tupling to faster homological stability, thus advancing understanding in topological combinatorics.
Contribution
It presents new notions of doubling and r-tupling for simplicial complexes, along with connectivity results and their implications for homological stability.
Findings
Connectivity results for doubled and r-tupled complexes
r-tupling accelerates homological stability
Relates combinatorial constructions to topological stability
Abstract
We introduce the notion of doubling and r-tupling for simplicial complexes, a notion reminiscent to that of matching complexes in graph theory. We prove a connectivity result for such complexes and relate r-tupling to stabilizing r times faster in homological stability.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Advanced Graph Theory Research · Homotopy and Cohomology in Algebraic Topology