TL;DR
This paper constructs a finite 2-complex that shares the fundamental group and Euler characteristic with a Klein bottle with a bubble but is homotopically distinct from it.
Contribution
It demonstrates the existence of a homotopically distinct finite 2-complex with the same fundamental group and Euler characteristic as a Klein bottle with a bubble.
Findings
Existence of a finite 2-complex with specified properties
Homotopically distinct from the Klein bottle with a bubble
Addresses a previously unresolved question
Abstract
We resolve the question of the existence of a finite 2-complex with the same fundamental group and Euler characteristic as a Klein bottle with a bubble, but homotopically distinct to it.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology · Mathematical Dynamics and Fractals