Cohomology at infinity and the well-rounded retract for general Linear Groups

Mathematics – Representation Theory

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Scientific paper

Let $\bold G$ be a reductive algebraic group defined over $\Q$, and let $\Gamma$ be an arithmetic subgroup of $\bold G(\Q)$. Let $X$ be the symmetric space for $\bold G(\R)$, and assume $X$ is contractible. Then the cohomology (mod torsion) of the space $X/\Gamma$ is the same as the cohomology of $\Gamma$. In turn, $X/\Gamma$ will have the same cohomology as $W/\Gamma$, if $W$ is a ``spine'' in $X$. This means that $W$ (if it exists) is a deformation retract of $X$ by a $\Gamma$-equivariant deformation retraction, that $W/\Gamma$ is compact, and that $\dim W$ equals the virtual cohomological dimension (vcd) of $\Gamma$. Then $W$ can be given the structure of a cell complex on which $\Gamma$ acts cellularly, and the cohomology of $W/\Gamma$ can be found combinatorially.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Cohomology at infinity and the well-rounded retract for general Linear Groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Cohomology at infinity and the well-rounded retract for general Linear Groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cohomology at infinity and the well-rounded retract for general Linear Groups will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-194957

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.