Homology with multiplevalued functions applied to fixed points
Author:
Richard Jerrard
Journal:
Trans. Amer. Math. Soc. 213 (1975), 407427
MSC:
Primary 55C20
Erratum:
Trans. Amer. Math. Soc. 218 (1976), 406.
MathSciNet review:
0380778
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Abstract: Certain multiplevalued functions (mfunctions) are defined and a homology theory based upon them is developed. In this theory a singular simplex is an mfunction from a standard simplex to a space and an mfunction from one space to another induces a homomorphism of homology modules. In a family of functions indexed by the fixed points of are taken to be the images at x of a multiplevalued function . In certain circumstances is an mfunction, giving information about the behavior of the fixed points of as x varies over X. These facts are applied to selfmaps of products of compact polyhedra and the question of whether such a product has the fixed point property for continuous functions is essentially reduced to the question of whether one of its factors has the fixed point property for mfunctions. Some light is thrown on the latter problem by using the homology theory to prove a Lefschetz fixed point theorem for mfunctions.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197503807786
PII:
S 00029947(1975)03807786
Article copyright:
© Copyright 1975
American Mathematical Society
