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2021 Iteration of functions and contractibility of acyclic 2-complexes
Ian J. Leary
Publ. Mat. 65(1): 309-318 (2021). DOI: 10.5565/PUBLMAT6512110

Abstract

We show that there can be no algorithm to decide whether infinite recursively described acyclic aspherical $2$-complexes are contractible. We construct such a complex that is contractible if and only if the Collatz conjecture holds.

Funding Statement

Partially supported by a Research Fellowship from the Leverhulme Trust. This work was started at MSRI, Berkeley, where research is supported by the National Science Foundation under Grant No. DMS-1440140.

Citation

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Ian J. Leary. "Iteration of functions and contractibility of acyclic 2-complexes." Publ. Mat. 65 (1) 309 - 318, 2021. https://doi.org/10.5565/PUBLMAT6512110

Information

Received: 2 October 2019; Revised: 23 March 2020; Published: 2021
First available in Project Euclid: 11 December 2020

MathSciNet: MR4185835
Digital Object Identifier: 10.5565/PUBLMAT6512110

Subjects:
Primary: 57M07
Secondary: 20F10

Keywords: $2$-complex , Collatz function , contractibility , iteration

Rights: Copyright © 2021 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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Vol.65 • No. 1 • 2021
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