Title  AN ALTERNATIVE CONSTRUCTION OF THE KAN LOOP GROUP 
Publication Type  Journal Article 
Year of Publication  2016 
Authors  Kim, Y 
Journal  International Electronic Journal of Pure and Applied Mathematics 
Volume  10 
Issue  2 
Start Page  161 
Pagination  6 
Date Published  11/2016 
Type of Article  scientific: mathematics 
ISSN  13140744 
Keywords  bisimplicial set, loop group, skeleton functor 
Abstract  Waldhausen 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 Waldhausenâ€™s simplicial graphs. Then we prove that in case of dimension 1, our construction defines the Kan loop group as with Waldhausenâ€™s.

URL  http://www.e.ijpam.eu/contents/articles/201601002006.pdf 
DOI  10.12732/iejpam.v10i2.6 
Short Title  AN ALTERNATIVE CONSTRUCTION OF THE KAN LOOP GROUP 
Alternate Journal  IeJPAM 
Refereed Designation  Refereed 