تقرير
Canonical lifts of the Johnson homomorphisms to the Torelli groupoid
| العنوان: | Canonical lifts of the Johnson homomorphisms to the Torelli groupoid |
|---|---|
| المؤلفون: | Bene, Alex James, Kawazumi, Nariya, Penner, R. C. |
| سنة النشر: | 2007 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Geometric Topology, 32G15, 57M99, 14H10, 57N05, 20F99 |
| الوصف: | 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 $\tau_m$, 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 $\tau_2$ 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 $\tau_m$, for $m\leq 3$. Comment: 38 pages, 6 figures |
| نوع الوثيقة: | Working Paper |
| الوصول الحر: | http://arxiv.org/abs/0707.2984Test |
| رقم الانضمام: | edsarx.0707.2984 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |