Homology and Fixed Points
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In this chapter we develop the algebraic and geometric notions needed to formulate and prove the main result, the Lefschetz-Hopf theorem for polyhedra. We further illustrate the use of homology by studying the special case of maps S n → S n , showing that the Brouwer degree of a map not only completely characterizes its homotopy behavior, but also gives considerable information about special topological features that such a map may have. We come full circle with the beginning of the last chapter by deriving Borsuk’s antipodal theorem within this homological framework.
KeywordsVector Field Exact Sequence Simplicial Complex Periodic Point Homology Group
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