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Concordance of Morse functions on manifolds

Hold Date
2023-01-27 15:10〜2023-01-27 15:40
Object person
Ryosuke Ota (Kyushu University)

Fold cobordism of Morse functions on smooth closed manifolds is an equivalence relation defined by using cobordisms of manifolds and fold maps. Given two Morse functions, it is important to decide whether they are concordant or not, and this problem was first solved for surfaces and then for manifolds of general dimensions by Ikegami–Saeki, Kalmár, and Ikegami. On the other hand, for Morse functions on the same manifold, we can consider a stronger equivalence relation called concordance. In this talk, a necessary and sufficient condition for given two Morse functions on a manifold to be concordant is presented, and is compared with the cobordism criterion.