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Homotopic distance between maps

Part of: Fiber spaces and bundles Classical Topics in Algebraic Topology Homotopy theory Artificial intelligence (68Txx)

Published online by Cambridge University Press:  22 February 2021

E. MACÍAS–VIRGÓS  and
D. MOSQUERA–LOIS
E. MACÍAS–VIRGÓS
Affiliation:
Institute of Mathematics, University of Santiago de Compostela, Avda. Lope Gómez de Marzoa s/n. Campus Sur, Santiago de Compostela, 15782Spain. e-mails: quique.macias@usc.es, david.mosquera.lois@usc.es
D. MOSQUERA–LOIS
Affiliation:
Institute of Mathematics, University of Santiago de Compostela, Avda. Lope Gómez de Marzoa s/n. Campus Sur, Santiago de Compostela, 15782Spain. e-mails: quique.macias@usc.es, david.mosquera.lois@usc.es
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Abstract

We show that well-known invariants like Lusternik–Schnirelmann category and topological complexity are particular cases of a more general notion, that we call homotopic distance between two maps. As a consequence, several properties of those invariants can be proved in a unified way and new results arise.

MSC classification

Primary: 55M30: Ljusternik-Schnirelman (Lyusternik-Shnirel'man) category of a space
Secondary: 55M99: None of the above, but in this section 55P99: None of the above, but in this section 55R10: Fiber bundles 55P45: $H$-spaces and duals 68T40: Robotics
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 172 , Issue 1 , January 2022 , pp. 73 - 93
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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Footnotes

†

Partially supported by MINECO Spain research project MTM2016-78647-P and by Xunta de Galicia ED431C 2019/10 with FEDER funds.

‡

Partially supported by Ministerio de Ciencia, Innovación y Universidades, grant FPU17/03443.

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