Canonical lifts of the Johnson homomorphisms to the Torelli groupoid
| dc.creator | Bene, Alex James | |
| dc.creator | Kawazumi, Nariya | |
| dc.creator | Penner, R. C. | |
| dc.date | 2007-07-20 | |
| dc.date.accessioned | 2026-07-07T08:19:20Z | |
| dc.date.available | 2026-07-07T08:19:20Z | |
| dc.description | We prove that every trivalent marked bordered fatgraph comes equipped with a canonical generalized Magnus expansion in the sense of Kawazumi. This Magnus expansion is used to give canonical lifts of the higher Johnson homomorphisms $τ_m$, for $m\geq 1$, to the Torelli groupoid, and we provide a recursive combinatorial formula for tensor representatives of these lifts. In particular, we give an explicit 1-cocycle in the dual fatgraph complex which lifts $τ_2$ and thus answer affirmatively a question of Morita-Penner. To illustrate our techniques for calculating higher Johnson homomorphisms in general, we give explicit examples calculating $τ_m$, for $m\leq 3$. | |
| dc.description | 38 pages, 6 figures | |
| dc.identifier | https://arxiv.org/abs/0707.2984 | |
| dc.identifier | http://arxiv.org/abs/0707.2984 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134730 | |
| dc.subject | Geometric Topology | |
| dc.subject | 32G15; 57M99; 14H10; 57N05; 20F99 | |
| dc.title | Canonical lifts of the Johnson homomorphisms to the Torelli groupoid | |
| dc.type | text |