Fundamentals of Algebraic Topology pp 127-138 | Cite as

# Homotopy Theory

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## Abstract

Let *X* be a space and let *x* _{0} be a point in *X*. In section 2.1 we introduced the fundamental group \(\pi _{1}(X,x_{0})\). In this chapter we introduce the *homotopy groups* \(\pi _{n}(X,x_{0})\) for every *n* ≥ 0. Also, if (*X*, *A*, *x* _{0}) is a triple, i.e., if *A* is a subspace of *X* and *x* _{0} is a point in *A*, we have the *relative homotopy groups* \(\pi _{n}(X,A,x_{0})\) for every *n* ≥ 1.

## Keywords

Fundamental Group Distinguished Element Homotopy Class Homotopy Group Homotopy Theory
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 International Publishing Switzerland 2014