The Birman-Craggs-Johnson homomorphism and abelian cycles in the Torelli group
| dc.creator | Brendle, Tara E. | |
| dc.creator | Farb, Benson | |
| dc.date | 2006-01-09 | |
| dc.date.accessioned | 2026-07-07T06:58:38Z | |
| dc.date.available | 2026-07-07T06:58:38Z | |
| dc.description | In the 1970s, Birman-Craggs-Johnson used Rochlin's invariant for homology 3-spheres to construct a remarkable surjective homomorphism sigma:I_{g,1}->B_3, where I_{g,1} is the Torelli group and B_3 is a certain F_2-vector space of Boolean (square-free) polynomials. By pulling back cohomology classes and evaluating them on abelian cycles, we construct 16g^4 + O(g^3) dimensions worth of nontrivial elements of H^2(I_{g,1}, F_2) which cannot be detected rationally. These classes in fact restrict to nontrivial classes in the cohomology of the subgroup K_{g,1} < I_{g,1} generated by Dehn twists about separating curves. We also use the ``Casson-Morita algebra'' and Morita's integral lift of the Birman-Craggs-Johnson map restricted to K_{g,1} to give the same lower bound on H^2(K_{g,1},Z). | |
| dc.description | 21 pages, 7 figures | |
| dc.identifier | https://arxiv.org/abs/math/0601163 | |
| dc.identifier | http://arxiv.org/abs/math/0601163 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107438 | |
| dc.subject | Geometric Topology | |
| dc.subject | Group Theory | |
| dc.subject | 57M07 | |
| dc.title | The Birman-Craggs-Johnson homomorphism and abelian cycles in the Torelli group | |
| dc.type | text |