Cut numbers of 3-manifolds

Details Cut numbers of 3-manifolds Cut numbers of 3-manifolds

2001-12-12

arxiv.org/abs/math/0112106v2

Mathematics

Geometric Topology

15 pages, no figures, to appear in Trans. of AMS

Scientific paper

The cut number of a manifold M, c(M), is the largest number of disjoint two-sided hypersurfaces in M which do not separate M. Equivalently, it is the largest rank of a free group being an epimorphic image of pi_1(M). We investigate the relations between the cut number and the first Betti number, b_1(M), of 3-manifolds M. We prove that the cut number of a ``generic'' 3-manifold is at most 2. This is a rather unexpected result since it is very hard to construct specific examples of 3-manifolds with with large b_1(M) and small c(M). On the other hand, we prove that for any complex semisimple Lie algebra g there exists a 3-manifold M with b_1(M)=dim g and c(M)<=rank g. Such manifolds can be explicitly constructed.

Affiliated with

Also associated with

No associations

Rating

Cut numbers of 3-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 Cut numbers of 3-manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cut numbers of 3-manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-82591