{"_buckets": {"deposit": "c433df9f-a76f-4945-a785-edba43c3e5be"}, "_deposit": {"id": "21762", "owners": [], "pid": {"revision_id": 0, "type": "depid", "value": "21762"}, "status": "published"}, "_oai": {"id": "oai:soar-ir.repo.nii.ac.jp:00021762", "sets": ["1169:1170"]}, "author_link": ["110274", "110275", "110276"], "item_1628147817048": {"attribute_name": "\u51fa\u7248\u30bf\u30a4\u30d7", "attribute_value_mlt": [{"subitem_version_resource": "http://purl.org/coar/version/c_ab4af688f83e57aa", "subitem_version_type": "AM"}]}, "item_6_biblio_info_6": {"attribute_name": "\u66f8\u8a8c\u60c5\u5831", "attribute_value_mlt": [{"bibliographicIssueDates": {"bibliographicIssueDate": "2018-12-15", "bibliographicIssueDateType": "Issued"}, "bibliographicPageEnd": "790", "bibliographicPageStart": "723", "bibliographicVolumeNumber": "340", "bibliographic_titles": [{"bibliographic_title": "ADVANCES IN MATHEMATICS"}]}]}, "item_6_description_20": {"attribute_name": "\u6284\u9332", "attribute_value_mlt": [{"subitem_description": "The aim of this paper is to develop a refinement of Forman\u0027s 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\u0027s 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\u0027s 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\u0027s gradient flows is the existence of a partial order on the set of flow paths, from which a 2-category C(mu) is constructed. 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This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/."}]}, "item_6_select_64": {"attribute_name": "\u8457\u8005\u7248\u30d5\u30e9\u30b0", "attribute_value_mlt": [{"subitem_select_item": "author"}]}, "item_6_source_id_35": {"attribute_name": "ISSN", "attribute_value_mlt": [{"subitem_source_identifier": "0001-8708", "subitem_source_identifier_type": "ISSN"}]}, "item_6_source_id_39": {"attribute_name": "NII ISSN", "attribute_value_mlt": [{"subitem_source_identifier": "0001-8708", "subitem_source_identifier_type": "ISSN"}]}, "item_6_source_id_40": {"attribute_name": "\u66f8\u8a8c\u30ec\u30b3\u30fc\u30c9ID", "attribute_value_mlt": [{"subitem_source_identifier": "AA00513055", "subitem_source_identifier_type": "NCID"}]}, "item_6_text_69": {"attribute_name": "wosonly authkey", "attribute_value_mlt": [{"subitem_text_value": "2-CATEGORIES; COMPLEXES"}]}, "item_6_text_70": {"attribute_name": "wosonly keywords", "attribute_value_mlt": [{"subitem_text_value": "The aim of this paper is to develop a refinement of Forman\u0027s 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\u0027s 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\u0027s 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\u0027s 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\u0027s. (C) 2018 Elsevier Inc. 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