Can I read Making Equivariant Maps Fixed Point Free on EtoBox?

Making Equivariant Maps Fixed Point Free by Davide L. Ferrario is a Mathematics article available to read on EtoBox.

What is Making Equivariant Maps Fixed Point Free about?

One of the most crucial questions in (Nielsen) equivariant fixed point theory is the following. Let G be a compact Lie group, and X a G-space. Given an equivariant map f : X → X such that for each subgroup H ⊂ G, f H : X H → X H can be deformed to be fixed point free by a compactly fixed homotopy, is it true that f can be deformed by a compactly fixed G-homotopy to a fixed point free map? Furthermore, if the Nielsen numbers N(f H ) vanish, is it true that f can be equivariantly deformed to be fixed point free (converse of the Lefschetz property for n G )? Fadell and Wong [Pacific J. Math. 132 (1988) 277-281] gave positive answers to these questions, under the hypothesis that dim(X H s ) + 2 dim(X H ) (Codimension Hypothesis). In this paper we prove that if f is isovariant, and the group G is 2-split, then the converse of the Lefschetz Property for n G holds for G-manifolds of dimension = 2. We also give a counter-example that illustrates why in general the Codimension Hypothesis cannot be removed from the main result of Fadell and Wong, unless assuming further hypotheses.

Who reads Making Equivariant Maps Fixed Point Free?

Author

Davide L. Ferrario

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0166-8641)

Published

2001

Language

EN

Field

Mathematics (Physical Sciences)