Decomposing Perfect Discrete Morse Functions on Connected Sums of 3-manifolds

2018/04/03 by Neža Mramor Kosta, Kosta, Neza Mramor, Mehmetci̇k Pamuk +3
Computer Science · Mathematics · #Topological and Geometric Data Analysis #Homotopy and Cohomology in Algebraic Topology #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1804.00783

Abstract

In this paper, we show that if a closed, connected, oriented 3-manifold M = M1#M2 admits a perfect discrete Morse function, then one can decompose this function as perfect discrete Morse functions on M₁ and M₂. We also give an explicit construction of a separating sphere on M corresponding to such a decomposition.

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