 

James West
Absolute retract involutions of Hilbert cubes: Fixed point sets of infinite codimension view print


Published: 
March 4, 2018 
Keywords: 
Hilbert cube, involution, absolute retract 
Subject: 
Primary: 57N20, 54C55; Secondary: 57S17, 54C15 


Abstract
Let α :Q→ Q be an involution of a Hilbert cube with fixed point set
Q^{α} that has Property Z in Q.
The first main result of this paper is Theorem 3.1: Assume that (Q,α)
is an absolute retract in the category of metric spaces with involutions and
equivariant maps. If T⊆ Q is an equivariant retract of Q
containing Q^{α} that is an inequivariant Zset in Q, then for any
equivariant retraction r:Q→ T, Q is equivariantly homeomorphic with
the mapping cylinder M(r;T) of r reduced at T. The second main
result is part of Theorem 3.3:
Q^{α} is an equivariant strong deformation retract of Q if and
only if Q is equivariantly homeomorphic with
Q^{α}× Π_{i≧1}I_{i} equipped with the involution that reflects each
interval coordinate I_{i} across its midpoint.


Author information
Department of Mathematics, Cornell University, Ithaca, NY 140534201, USA
west@math.cornell.edu

