naa a22 4500 510782884 CHVBK 20180411083253.0 cr unu---uuuuu 180411e20130601xx s 000 0 eng 10.1007/s11856-012-0075-3 doi (NATIONALLICENCE)springer-10.1007/s11856-012-0075-3 Cohomology of the hyperelliptic Torelli group [Elektronische Daten] [Tara Brendle, Leah Childers, Dan Margalit] Let SI(S g ) denote the hyperelliptic Torelli group of a closed surface S g of genus g. This is the subgroup of the mapping class group of S g consisting of elements that act trivially on H 1(S g ; ℤ) and that commute with some fixed hyperelliptic involution of S g . We prove that the cohomological dimension of SI(S g ) is g − 1 when g ≥ 1. We also show that H g−1(SI(S g ); ℤ) is infinitely generated when g ≥ 2. In particular, SI(S 3) is not finitely presentable. Finally, we apply our main results to show that the kernel of the Burau representation of the braid group B n at t = −1 has cohomological dimension equal to the integer part of n/2, and it has infinitely generated homology in this top dimension. Hebrew University Magnes Press, 2013 Brendle Tara School of Mathematics & Statistics University Gardens, University of Glasgow, G12 8QW, Scotland, UK aut Childers Leah Pittsburg State University, 224 Yates Hall, 66762-7502, Pittsburg, KS, USA aut Margalit Dan School of Mathematics, Georgia Institute of Technology, 686 Cherry St., 30332, Atlanta, GA, USA aut Israel Journal of Mathematics Springer US; http://www.springer-ny.com 195/2(2013-06-01), 613-630 0021-2172 195:2<613 2013 195 11856 https://doi.org/10.1007/s11856-012-0075-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0075-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Brendle Tara School of Mathematics & Statistics University Gardens, University of Glasgow, G12 8QW, Scotland, UK aut NATIONALLICENCE 700 1- Childers Leah Pittsburg State University, 224 Yates Hall, 66762-7502, Pittsburg, KS, USA aut NATIONALLICENCE 700 1- Margalit Dan School of Mathematics, Georgia Institute of Technology, 686 Cherry St., 30332, Atlanta, GA, USA aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 195/2(2013-06-01), 613-630 0021-2172 195:2<613 2013 195 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer