論文

査読有り
2017年10月

Directed Homology Theories and Eilenberg-Steenrod Axioms

APPLIED CATEGORICAL STRUCTURES
  • Jérémy Dubut
  • ,
  • Eric Goubault
  • ,
  • Jean Goubault-Larrecq

25
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
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
  • DOI : 10.1007/s10485-016-9438-y
  • ISSN : 0927-2852
  • eISSN : 1572-9095
  • DBLP ID : journals/acs/DubutGG17
  • Web of Science ID : WOS:000411335100003

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