1. CJM 2001 (vol 53 pp. 212)
 Puppe, V.

Group Actions and Codes
A $\mathbb{Z}_2$action with ``maximal number of isolated fixed
points'' ({\it i.e.}, with only isolated fixed points such that
$\dim_k (\oplus_i H^i(M;k)) =M^{\mathbb{Z}_2}, k = \mathbb{F}_2)$
on a $3$dimensional, closed manifold determines a binary selfdual
code of length $=M^{\mathbb{Z}_2}$. In turn this code determines
the cohomology algebra $H^*(M;k)$ and the equivariant cohomology
$H^*_{\mathbb{Z}_2}(M;k)$. Hence, from results on binary selfdual
codes one gets information about the cohomology type of $3$manifolds
which admit involutions with maximal number of isolated fixed points.
In particular, ``most'' cohomology types of closed $3$manifolds do
not admit such involutions. Generalizations of the above result are
possible in several directions, {\it e.g.}, one gets that ``most''
cohomology types (over $\mathbb{F}_2)$ of closed $3$manifolds do
not admit a nontrivial involution.
Keywords:Involutions, $3$manifolds, codes Categories:55M35, 57M60, 94B05, 05E20 
