On Changing Fixed Points and Coincidences to Roots
Copyright policy )On Changing Fixed Points and Coincidences to Roots
The coincidence problem, finding solutions to f ( x ) = g ( x ) f(x) = g(x) , can sometimes be converted to a root problem, finding solutions to σ ( x ) = a \sigma (x) = a . As an application, we show that for any two maps f , g : M → M , N ( f , g ) = | L ( f , g ) | f,g:M \to M,N(f,g) = |L(f,g)| where M M is a compact connected nilmanifold, N ( f , g ) N(f,g) and L ( f , g ) L(f,g) are the Nielsen and Lefschetz numbers, respectively, of f f and g g . This result in the case where g g is the identity is due to D. Anosov.
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roots, Fixed points and coincidences in algebraic topology, coincidences, Lefschetz number, Topological manifolds, nilmanifold, Nielsen number, Finite groups of transformations in algebraic topology (including Smith theory)
roots, Fixed points and coincidences in algebraic topology, coincidences, Lefschetz number, Topological manifolds, nilmanifold, Nielsen number, Finite groups of transformations in algebraic topology (including Smith theory)
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