The Lefschetz Fixed Point Theorem
نویسنده
چکیده
The Lefschetz Fixed Point Theorem generalizes a collection of fixed point theorems for different topological spaces, including maps on the n-sphere and the n-disk. Although the theorem is easily written in terms of compact manifolds, in this paper we will work entirely with topological spaces that are simplicial complexes or retracts of simplicial complexes. After developing the fundamentals of simplicial approximation, we will present a proof of the Lefschetz fixed point theorem and apply the theorem to maps on several topological spaces.
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