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AN ALTERNATIVE CONSTRUCTION OF THE KAN LOOP GROUP

TitleAN ALTERNATIVE CONSTRUCTION OF THE KAN LOOP GROUP
Publication TypeJournal Article
Year of Publication2016
AuthorsKim, Y
JournalInternational Electronic Journal of Pure and Applied Mathematics
Volume10
Issue2
Start Page161
Pagination6
Date Published11/2016
Type of Articlescientific: mathematics
ISSN1314-0744
Keywordsbisimplicial set, loop group, skeleton functor
AbstractWaldhausen described the construction of the Kan loop group using simplicial graphs. He proves that the homotopy group of the simplicial graph he constructed is the Kan loop group. Motivated by his construction, we introduce a new construction of the Kan loop group using bisimlicial sets. We construct a sequence of bisimplicial sets, one for each dimension, then prove the properties similar to Waldhausen’s simplicial graphs. Then we prove that in case of dimension 1, our construction defines the Kan loop group as with Waldhausen’s.
URLhttp://www.e.ijpam.eu/contents/articles/201601002006.pdf
DOI10.12732/iejpam.v10i2.6
Short TitleAN ALTERNATIVE CONSTRUCTION OF THE KAN LOOP GROUP
Alternate JournalIeJPAM
Refereed DesignationRefereed