Construction of Bundles on Simplicial Sets and Transition Functions

Akyar B.

ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING, vol.36, no.6, pp.1071-1082, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 6
  • Publication Date: 2011
  • Doi Number: 10.1007/s13369-011-0101-5
  • Journal Name: ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1071-1082
  • Keywords: Simplicial set, Realization, Bundle theory, Transition function
  • Dokuz Eylül University Affiliated: No

Abstract

We give the definition of a bundle over a simplicial set in a similar way to that in general bundle theory. We define certain transition functions, called compatible transition functions, for the given bundle, as well as so-called admissible trivializations. Conversely, we give the description of an associated bundle over the realization of the simplicial set and trivializations for a given set of transition functions.