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  1. 040 理学部
  2. 0401 学術論文

Discrete Morse theory and classifying spaces

http://hdl.handle.net/10091/00022519
http://hdl.handle.net/10091/00022519
1e8ac472-8467-442c-8949-6b307b4eb706
名前 / ファイル ライセンス アクション
15K04870_02.pdf 15K04870_02.pdf (544.2 kB)
Item type 学術雑誌論文 / Journal Article(1)
公開日 2021-02-16
タイトル
タイトル Discrete Morse theory and classifying spaces
言語
言語 eng
DOI
関連識別子 https://doi.org/10.1016/j.aim.2018.10.016
関連名称 10.1016/j.aim.2018.10.016
キーワード
主題 Discrete Morse theory, Classifying space, Small category
資源タイプ
資源 http://purl.org/coar/resource_type/c_6501
タイプ journal article
著者 Nanda, Vidit

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Nanda, Vidit

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Tamaki, Dai

× Tamaki, Dai

Tamaki, Dai

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Tanaka, Kohei

× Tanaka, Kohei

Tanaka, Kohei

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信州大学研究者総覧へのリンク
氏名 Tamaki, Dai
URL https://soar-rd.shinshu-u.ac.jp/profile/ja.OafeOUkh.html
信州大学研究者総覧へのリンク
氏名 Tanaka, Kohei
URL https://soar-rd.shinshu-u.ac.jp/profile/ja.uaLFOmkV.html
出版者
出版者 ACADEMIC PRESS INC ELSEVIER SCIENCE
引用
内容記述 ADVANCES IN MATHEMATICS.340:723-790(2018)
書誌情報 ADVANCES IN MATHEMATICS

巻 340, p. 723-790, 発行日 2018-12-15
抄録
内容記述 The aim of this paper is to develop a refinement of Forman's discrete Morse theory. To an acyclic partial matching mu on a finite regular CW complex X, Forman introduced a discrete analogue of gradient flows. Although Forman's gradient flow has been proved to be useful in practical computations of homology groups, it is not sufficient to recover the homotopy type of X. Forman also proved the existence of a CW complex which is homotopy equivalent to X and whose cells are in one-to-one correspondence with the critical cells of mu but the construction is ad hoc and does not have a combinatorial description. By relaxing the definition of Forman's gradient flows, we introduce the notion of flow paths, which contains enough information to reconstruct the homotopy type of X, while retaining a combinatorial description. The critical difference from Forman's gradient flows is the existence of a partial order on the set of flow paths, from which a 2-category C(mu) is constructed. It is shown that the classifying space of C(mu) is homotopy equivalent to X by using homotopy theory of 2-categories. This result can be also regarded as a discrete analogue of the unpublished work of Cohen, Jones, and Segal on Morse theory in early 90's. (C) 2018 Elsevier Inc. All rights reserved.
資源タイプ(コンテンツの種類)
ISSN
収録物識別子タイプ ISSN
収録物識別子 0001-8708
書誌レコードID
収録物識別子タイプ NCID
収録物識別子 AA00513055
権利
権利情報 © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/.
出版タイプ
出版タイプ AM
出版タイプResource http://purl.org/coar/version/c_ab4af688f83e57aa
WoS
URL http://gateway.isiknowledge.com/gateway/Gateway.cgi?&GWVersion=2&SrcAuth=ShinshuUniv&SrcApp=ShinshuUniv&DestLinkType=FullRecord&DestApp=WOS&KeyUT=000451363700018
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Cite as

Nanda, Vidit, Tamaki, Dai, Tanaka, Kohei, 2018, Discrete Morse theory and classifying spaces: ACADEMIC PRESS INC ELSEVIER SCIENCE, 723–790 p.

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