### An example concerning equivariant deformations

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 $[\text{\rm{id}}_X]_{ Z_2}$.

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

#### Full Text:

FULL TEXT### Refbacks

- There are currently no refbacks.