EPARATION IN THE BNSR-INVARIANTS OF THE PURE BRAID GROUPS

被引:9
作者
Zaremsky, Matthew C. B. [1 ]
机构
[1] SUNY Binghamton, Dept Math Sci, Binghamton, NY 13902 USA
关键词
Braid group; BNSR-invariant; finiteness properties; MAPPING CLASS GROUP; SIGMA-INVARIANTS; DIMENSION;
D O I
10.5565/PUBLMAT6121702
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We inspect the BNSR-invariants Sigma(m)(P-n) of the pure braid groups P-n, using Morse theory. The BNS-invariants Sigma(1)(P-n) were previously computed by Koban, McCammond, and Meier. We prove that for any 3 <= m <= n, the inclusion Sigma(m-2)(P-n) subset of Sigma(m-3)(P-n) is proper, but Sigma(infinity)(P-n) = Sigma(n-2)(P-n). We write down explicit character classes in each relevant Sigma(m-3)(P-n)\Sigma(m-2)(P-n). In particular we get examples of normal subgroups N <= P-n with P-n/N congruent to Z such that N is of type Fm-3 but not Fm-2, for all 3 <= m <= n.
引用
收藏
页码:337 / 362
页数:26
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