Vanishing results for the cohomology of complex toric hyperplane complements

Details Vanishing results for the cohomology of complex toric hyperplane complements Vanishing results for the cohomology of complex toric hyperplane complements

2011-11-11

arxiv.org/abs/1111.2866v1

Mathematics

Algebraic Topology

14 pages. arXiv admin note: substantial text overlap with arXiv:math/0612404

Scientific paper

Suppose $\Cal R$ is the complement of an essential arrangement of toric hyperlanes in the complex torus $(\C^*)^n$ and $\pi=\pi_1(\Cal R)$. We show that $H^*(\Cal R;A)$ vanishes except in the top degree $n$ when $A$ is one of the following systems of local coefficients: (a) a system of nonresonant coefficients in a complex line bundle, (b) the von Neumann algebra $\cn\pi$, or (c) the group ring $\zz \pi$. In case (a) the dimension of $H^n$ is the Euler characteristic, $e(\Cal R)$, and in case (b) the $n^{\mathrm{th}}$ $\eltwo$ Betti number is also $e(\Cal R)$.

Affiliated with

Also associated with

No associations

Rating

Vanishing results for the cohomology of complex toric hyperplane complements 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 Vanishing results for the cohomology of complex toric hyperplane complements, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Vanishing results for the cohomology of complex toric hyperplane complements will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-2733