Contractible complexes and non-positive immersions
William Fisher
TL;DR
This paper presents examples of contractible complexes that do not admit non-positive immersions, disproving Wise's conjecture and highlighting limitations in the theory of such complexes.
Contribution
It provides the first known examples of contractible complexes lacking non-positive immersions, challenging previous assumptions in the field.
Findings
Examples of contractible complexes without non-positive immersions
Disproof of Wise's conjecture
Insights into the structure of contractible complexes
Abstract
We provide examples of contractible complexes which fail to have non-positive immersions and weak non-positive immersions, answering a conjecture of Wise in the negative.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Mathematical Dynamics and Fractals · Advanced Operator Algebra Research