A Fixed Point Theorem for Manifolds
Copyright policy )A Fixed Point Theorem for Manifolds
A Lefschetz type fixed point theorem is proved extending a recent theorem by Robert F. Brown. It deals with compact maps of the form f : ( M − U , X ) → ( M , M − U ) f:(M - U,X) \to (M,M - U) , where M M is an n n -manifold, X X is an ( n − 2 ) (n - 2) -connected ANR which is closed in M M and U U is an unbounded component of M − U M - U . The map f f defines maps u : M − U → M − U u:M - U \to M - U and v : M → M v:M \to M ; the Lefschetz numbers of u u and v v are defined and are shown to be equal; and if this number is nonzero then f f has a fixed point.
Fixed points and coincidences in algebraic topology, Topology of the Euclidean \(n\)-space, \(n\)-manifolds (\(4 \leq n \leq \infty\))
Fixed points and coincidences in algebraic topology, Topology of the Euclidean \(n\)-space, \(n\)-manifolds (\(4 \leq n \leq \infty\))
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