Braid groups of non-orientable surfaces and the Fadell-Neuwirth short exact sequence

Details Braid groups of non-orientable surfaces and the Fadell-Neuwirth short exact sequence Braid groups of non-orientable surfaces and the Fadell-Neuwirth short exact sequence

2009-04-25

arxiv.org/abs/0904.3962v1

Journal of Pure and Applied Algebra 214, 5 (2010) 667-677

Mathematics

Geometric Topology

17 pages

Scientific paper

10.1016/j.jpaa.2009.07.009

Let M be a compact, connected non-orientable surface without boundary and of genus g greater than or equal to 3. We investigate the pure braid groups P_n(M) of M, and in particular the possible splitting of the Fadell-Neuwirth short exact sequence 1 --> P_m(M {x_1,...,x_n}) --> P_{n+m}(M) --> P_n(M) --> 1, where m,n are positive integers, and the homomorphism p*:P_{n+m}(M) --> P_n(M) corresponds geometrically to forgetting the last m strings. This problem is equivalent to that of the existence of a section for the associated fibration p:F_{n+m}(M)} --> F_n(M) of configuration spaces, defined by p((x_1,...,x_n,..., x_{n+m}))= (x_1, ..., x_n). We show that p and p* admit a section if and only if n=1. Together with previous results, this completes the resolution of the splitting problem for surfaces pure braid groups.

Affiliated with

Also associated with

No associations

Rating

Braid groups of non-orientable surfaces and the Fadell-Neuwirth short exact sequence 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 Braid groups of non-orientable surfaces and the Fadell-Neuwirth short exact sequence, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Braid groups of non-orientable surfaces and the Fadell-Neuwirth short exact sequence will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-671280