Advertisement

Homotopy Groups

  • Davide L. Ferrario
  • Renzo A. Piccinini
Chapter
Part of the CMS Books in Mathematics book series (CMSBM)

Abstract

The Fundamental Theorem of Surfaces assures us that any connected compact surface is homeomorphic to one of the following closed surfaces: the two-dimensional sphere, a connected sum of tori, or a connected sum of real projective planes. We have seen that the homology groups of such closed surfaces are not isomorphic, and therefore, the surfaces under discussion cannot be homeomorphic. It is possible to arrive at this same result by computing another algebraic invariant of the polyhedra, the so-called fundamental group, which is clearly related to the first homology group. In what follows, we shall study such concepts in detail.

Keywords

Base Point Fundamental Group Simplicial Complex Homology Group Homotopy Class 
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.

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Dipartimento di Matematica e ApplicazioniUniversità di Milano-BicoccaMilanoItaly
  2. 2.Department of Mathematics and StatisticsDalhousie UniversityHalifaxCanada

Personalised recommendations