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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On changing fixed points and coincidences to roots

Authors: Robin Brooks and Peter Wong
Journal: Proc. Amer. Math. Soc. 115 (1992), 527-533
MSC: Primary 55M20
Correction: Proc. Amer. Math. Soc. 118 (1993), 1353-1354.
MathSciNet review: 1098397
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Abstract: The coincidence problem, finding solutions to $ f(x) = g(x)$, can sometimes be converted to a root problem, finding solutions to $ \sigma (x) = a$. As an application, we show that for any two maps $ f,g:M \to M,N(f,g) = \vert L(f,g)\vert$ where $ M$ is a compact connected nilmanifold, $ N(f,g)$ and $ L(f,g)$ are the Nielsen and Lefschetz numbers, respectively, of $ f$ and $ g$. This result in the case where $ g$ is the identity is due to D. Anosov.

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Keywords: Fixed points, coincidences, roots, Lefschetz number, Nielsen number, degree, nilmanifold
Article copyright: © Copyright 1992 American Mathematical Society

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