An example concerning equivariant deformations

Marek Izydorek, Antonio Vidal

DOI: http://dx.doi.org/10.12775/TMNA.2000.015

Abstract


We give an example of $Z_2$-space $X$ with a
property that the
identity map $\text{\rm{id}}_X:X\to X$ as well as its
restriction to the fixed point
set of the group action
$\text{\rm{id}}^{Z_2}:X^{Z_2}\to X^{Z_2}$ are
deformable to fixed point free
maps whereas there is no fixed point free
map in the equivariant homotopy
class of the identity $[\text{\rm{id}}_X]_{ Z_2}$.

Keywords


$Z_2$-space; equivariant deformations; fixed point free maps

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