Mathematics – Group Theory
Scientific paper
2001-11-14
Mathematics
Group Theory
54 pages, amscd
Scientific paper
We consider locally symmetric manifolds with a fixed universal covering, and construct for each such manifold M a simplicial complex R whose size is proportional to the volume of M. When M is non-compact, R is homotopically equivalent to M, while when M is compact, R is homotopically equivalent to M\N, where N is a finite union of submanifolds of fairly smaller dimensions. This expresses how the volume controls the topological structure of M, and yields concrete bounds for various finiteness statements which previously had no quantitative proofs. For example, it gives an explicit upper bound for the possible number of locally symmetric manifolds of volume bounded by v>0, and it yields an estimate for the size of a minimal presentation for the fundamental group of a manifold in terms of its volume. It also yields a number of new finiteness results.
No associations
LandOfFree
Homotopy type and volume of locally symmetric manifolds 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 Homotopy type and volume of locally symmetric manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Homotopy type and volume of locally symmetric manifolds will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-355776