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Discrete Morse theory and classifying spaces
http://hdl.handle.net/10091/00022519
http://hdl.handle.net/10091/000225191e8ac472-8467-442c-8949-6b307b4eb706
| 名前 / ファイル | ライセンス | アクション |
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15K04870_02.pdf (544.2 kB)
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| Item type | 学術雑誌論文 / Journal Article(1) | |||||||||||
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| 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
× Nanda, Vidit
× Tamaki, Dai
× 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 |
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| 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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