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Obstruction Theory

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Abstract

in this chapter we develop obstruction theory for the general lifting problem. A sequence of obstructions is defined whose vanishing is necessary and sufficient for the existence of a lifting. The kth obstruction in the sequence is defined if and only if all the lower obstructions are defined and vanish, in which case the vanishing of the kth obstruction is a necessary condition for definition of the (k + l)st obstruction.

Keywords

  • Obstruction Theory
  • Free Homotopy Class
  • Lift Problem
  • Weak Homotopy
  • Cohomology Operation

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  • DOI: 10.1007/978-1-4684-9322-1_9
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© 1966 Springer-Verlag New York, Inc.

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Spanier, E.H. (1966). Obstruction Theory. In: Algebraic Topology. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9322-1_9

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  • DOI: https://doi.org/10.1007/978-1-4684-9322-1_9

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-94426-5

  • Online ISBN: 978-1-4684-9322-1

  • eBook Packages: Springer Book Archive