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Abstract

we are now ready to extend the definition of homology to more general coefficients. In this framework the homology considered in the last chapter appears as the special case of integral coefficients. The extension is done in a purely algebraic way. Given a chain complex C and an abelian group G, their tensor product is the chain complex CG = {C q G, ∂ q ⊗ 1}, and the homology of CG is defined to be the homology of C, with coefficients G.

Keywords

  • Exact Sequence
  • Hopf Algebra
  • Chain Complex
  • Short Exact Sequence
  • Finite Type

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© 1966 Springer-Verlag New York, Inc.

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Spanier, E.H. (1966). Products. In: Algebraic Topology. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9322-1_6

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  • DOI: https://doi.org/10.1007/978-1-4684-9322-1_6

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-94426-5

  • Online ISBN: 978-1-4684-9322-1

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