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Homotopy

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Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

This chapter introduces the basic definitions of homotopy theory in a very limited setting. Our main purpose is to simplify the computation of homology groups by introducing the concept of deformation retraction, but we include a brief introduction to the fundamental group. This is intended more for the sake of literacy and for practice designing homotopies than as a complete disquisition, since I am assuming a limited exposure to the requisite group theory. We leave further study of the fundamental group to more advanced texts.

“The essence of mathematics is not to make simple things complicated, but to make complicated things simple.”

Gudder

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  • DOI: 10.1007/978-1-4612-0899-0_9
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© 1993 Springer Science+Business Media New York

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Kinsey, L.C. (1993). Homotopy. In: Topology of Surfaces. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0899-0_9

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  • DOI: https://doi.org/10.1007/978-1-4612-0899-0_9

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-6939-7

  • Online ISBN: 978-1-4612-0899-0

  • eBook Packages: Springer Book Archive