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タイトル: CUTTING AND PASTING OF MORSE FUNCTIONS (Research on topology and differential geometry using singularity theory of differentiable maps)
著者: WRAZIDLO, DOMINIK J.
キーワード: 57R45
57R90
57R60
57R65
58K15
57R56
Morse function
cobordism of smooth maps
$SKK$-group
発行日: Dec-2019
出版者: 京都大学数理解析研究所
誌名: 数理解析研究所講究録
巻: 2140
開始ページ: 36
終了ページ: 51
抄録: Cobordism groups of various types of Morse functions have been studied separately by several authors including Ikegami, Kalmar, Saeki, Yamamoto, and the author. In this article, we propose a conceptually new approach for studying cobordism groups of several types of Morse functions within a single unifying framework. Our method is crucially based on certain cutting and pasting relations for manifolds that have been used before to define SKK-groups of manifolds. We provide an explicit isomorphism between the cobordism group of Morse functions and SKK-groups. Moreover, we sketch an application of our framework to cobordism theory for Morse functions with boundary, and raise some problems for future study concerning Morse functions with index constraints and circle-valued Morse functions.
URI: http://hdl.handle.net/2433/254921
出現コレクション:2140 可微分写像の特異点論を用いたトポロジー・微分幾何学の研究

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