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EXISTENCE AND DEFORMABILITY OF TOPOLOGICAL MORSE FUNCTIONS

Part of: Topological manifolds

Published online by Cambridge University Press:  30 October 2025

INGRID IRMER Open the ORCID record for INGRID IRMER [Opens in a new window]
INGRID IRMER*
Affiliation:
SUSTech International Center for Mathematics, and Department of Mathematics, Southern University of Science and Technology , Shenzhen, PR China
*
e-mail: ingridmary@sustech.edu.cn
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Abstract

In the 1950s, Morse defined the analogue of Morse functions for topological manifolds. In many instances, when mathematicians are using techniques on topological manifolds that appear to be Morse-theoretic in nature, there is a topological Morse function implicit in the argument. Topological Morse functions are known to inherit most of the familiar properties of the usual (smooth) Morse functions, with two crucial exceptions: existence and deformability. This paper gives a simple construction of continuous families of topological Morse functions.

Keywords

Morse theorytopological manifoldconvex function

MSC classification

Primary: 57N99: None of the above, but in this section

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , First View , pp. 1 - 7
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc

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