Mitchener, P.D., Norouzizadeh, B. and Schick, T. (2020) Coarse homotopy groups. Mathematische Nachrichten, 293 (8). pp. 1515-1533. ISSN 0025-584X
Abstract
In this note on coarse geometry we revisit coarse homotopy. We prove that coarse homotopy indeed is an equivalence relation, and this in the most general context of abstract coarse structures. We introduce (in a geometric way) coarse homotopy groups. The main result is that the coarse homotopy groups of a cone over a compact simplicial complex coincide with the usual homotopy groups of the underlying compact simplicial complex.
To prove this we develop geometric triangulation techniques for cones which we expect to be of relevance also in different contexts.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020 The Authors. Mathematische Nachrichten published by Wiley‐VCH Verlag GmbH & Co. KGaA. This is an open access article under the terms of the Creative Commons Attribution License, (http://creativecommons.org/licenses/by/4.0/) which permits use, distribution and reproduction in any medium, provided the original work is properly cited. |
Keywords: | coarse algebraic topology; coarse geometry; geometric triangulations; homotopy groups; simplicial geometry |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 06 Nov 2019 14:51 |
Last Modified: | 17 Dec 2021 11:01 |
Status: | Published |
Publisher: | Wiley |
Refereed: | Yes |
Identification Number: | 10.1002/mana.201800523 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:152944 |