Advertisement

Deeper Structure: Simplicial Sets

Chapter
  • 1.8k Downloads
Part of the Universitext book series (UTX)

Abstract

In this chapter we will develop some further properties necessary to understand simplicial sets. In order to control the weak equivalences we introduce two classes of maps: fibrations and cofibrations. These maps formalize “obstruction theory”, or rather they tell us when existence of liftings can be expected. This is intimately connected with the fact that weak equivalences are not isomorphisms, although they become so in the homotopy category.

Keywords

Simplicial Group Homotopy Group Algebraic Topology Weak Equivalence Homotopy Category 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BergenBergenNorway

Personalised recommendations