Decomposing perfect discrete Morse functions on connected sum of 3-manifolds

摘要

In this paper, we show that if a closed, connected, oriented 3-manifold M = M-1 # M-2 admits a perfect discrete Morse function, then one can decompose this function as perfect discrete Morse functions on M-1 and M-2. We also give an explicit construction of a separating sphere on M corresponding to such a decomposition. (C) 2019 Elsevier B.V. All rights reserved.