Homology, Homotopy and Applications

Volume 20 (2018)

Number 1

Perfect discrete Morse functions on connected sums

Pages: 219 – 236

DOI: https://dx.doi.org/10.4310/HHA.2018.v20.n1.a13

Authors

Hanife Varli (Mathematics Department, Middle East Technical University, Ankara, Turkey)

Mehmetcik Pamuk (Mathematics Department, Middle East Technical University, Ankara, Turkey)

Neža Mramor Kosta (Faculty of Computer and Information Science and Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Slovenia)

Abstract

We study perfect discrete Morse functions on closed, connected, oriented $n$-dimensional manifolds.We show how to compose such functions on connected sums of manifolds of arbitrary dimensions and how to decompose them on connected sums of closed oriented surfaces.

Keywords

perfect discrete Morse function, discrete vector field, connected sum

2010 Mathematics Subject Classification

37E35, 57R70

Received 2 December 2016

Received revised 5 October 2017

Published 31 January 2018