分野別セミナー

拡大版九大ポロジーセミナー
開催日：1月28日(火)
場所：W1-D-725
プログラム：
13:00〜14:00 北澤直樹氏（九州大学）
14:30〜15:30 小島道氏（九州大学）
16:00〜17:00 Boldizsar Kalmar 氏（Eotvos Lorand University/Budapest University of Technology and Economics）
講演はすべて英語です。

【講演題目】Cobordism group of Morse-Bott functions on surfaces
【開催期間】1月28日(火) 16:00〜17:00
【場所】W1-D-725
【講師】Boldizsar Kalmar 氏（Eotvos Lorand University/Budapest University of Technology and Economics）
【講演要旨】We study Morse-Bott functions on surfaces and compute their cobordism group. We also prove some
formulas about the relation of the numbers of different singularity types of a Morse-Bott function on a surface.
In order to compute the cobordism group of Morse-Bott functions, similarly to the computation of cobordism groups of Morse functions, we transform the problem of Morse-Bott functions into a problem of maps from graphs to the
real line and maps from 2-dimensional polyhedra to the plane. This transformation is realized by using Stein
factorization in a way that taking the Stein factorization of a cobordism between two Morse-Bott functions provides a cobordism in an abstract sense between the Reeb functions of the two Morse-Bott functions. For obtaining formulas about the numbers of different singularity types, we construct a set of generators for the cobordism group and compute the numbers of singularities on each of the generators to get our equations between them.