2017年10月
Directed Homology Theories and Eilenberg-Steenrod Axioms
APPLIED CATEGORICAL STRUCTURES
- ,
- ,
- 巻
- 25
- 号
- 5
- 開始ページ
- 775
- 終了ページ
- 807
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1007/s10485-016-9438-y
- 出版者・発行元
- SPRINGER
In this paper, we define and study a homology theory, that we call "natural homology", which associates a natural system of abelian groups to every space in a large class of directed spaces and precubical sets. We show that this homology theory enjoys many important properties, as an invariant for directed homotopy. Among its properties, we show that subdivided precubical sets have the same homology type as the original ones ; similarly, the natural homology of a precubical set is of the same type as the natural homology of its geometric realization. By same type we mean equivalent up to some form of bisimulation, that we define using the notion of open map. Last but not least, natural homology, for the class of spaces we consider, exhibits very important properties such as Hurewicz theorems, and most of Eilenberg-Steenrod axioms, in particular the dimension, homotopy, additivity and exactness axioms. This last axiom is studied in a general framework of (generalized) exact sequences.
- リンク情報
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- DOI
- https://doi.org/10.1007/s10485-016-9438-y
- DBLP
- https://dblp.uni-trier.de/rec/journals/acs/DubutGG17
- Web of Science
- https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000411335100003&DestApp=WOS_CPL
- URL
- http://dblp.uni-trier.de/db/journals/acs/acs25.html#journals/acs/DubutGG17
- ID情報
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- DOI : 10.1007/s10485-016-9438-y
- ISSN : 0927-2852
- eISSN : 1572-9095
- DBLP ID : journals/acs/DubutGG17
- Web of Science ID : WOS:000411335100003