A method of combining fixed points

Author:
Roger Waggoner

Journal:
Proc. Amer. Math. Soc. **51** (1975), 191-197

MSC:
Primary 54H25; Secondary 57C05

DOI:
https://doi.org/10.1090/S0002-9939-1975-0402713-X

MathSciNet review:
0402713

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Abstract: It is now well known that in the category of finite polyhedra the fixed point property is not preserved by the operations of suspension, Cartesian product, adjunction along a segment, and join. Thus far none of the examples given have involved polyhedra of dimension 2. It is shown in this paper that two fixed points and of a self-map of a polyhedron can be combined in a certain way if a certain criterion is satisfied by the -image of a path from to . Several corollaries follow, one of which is that if is a finite simply connected -polyhedron with no local separating points, , and has a -simplex such that is cyclic, then fails to have the fixed point property. This eliminates many -dimensional polyhedra from consideration as examples.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1975-0402713-X

Keywords:
Fixed point property,
Lefschetz number,
fixed point index

Article copyright:
© Copyright 1975
American Mathematical Society