|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'501'711
Articles rated: 2609
19 April 2024 |
|
| | | | |
|
Article forum
| |
|
|
Relative moduli spaces of complex structures: an example | | Yurii M. Burman
; | | Date: |
4 Mar 1999 | | Subject: | Differential Geometry; Combinatorics | math.DG math.CO | | Affiliation: | Independent University of Moscow | | Abstract: | Let M and N be even-dimensional oriented real manifolds, and $u:M o N$ be a smooth mapping. A pair of complex structures at M and N is called u-compatible if the mapping u is holomorphic with respect to these structures. The quotient of the space of u-compatible pairs of complex structures by the group of u-equivariant pairs of diffeomorphisms of M and N is called a moduli space of u-equivariant complex structures. The paper contains a description of the fundamental group G of this moduli space in the following case: $N = CP^1, M subset CP^2$ is a hyperelliptic genus g curve given by the equation $y^2 = Q(x)$ where Q is a generic polynomial of degree 2g+1, and $u(x,y) = y^2$. The group G is a kernel of several (equivalent) actions of the braid-cyclic group $BC_{2g}$ on 2g strands. These are: an action on the set of trees with 2g numbered edges, an action on the set of all splittings of a (4g+2)-gon into numbered nonintersecting quadrangles, and an action on a certain set of subgroups of the free group with 2g generators. $G_{2g} subset BC_{2g}$ is a subgroup of the index $(2g+1)^{2g-2}$. Key words: Teichmüller spaces, Lyashko-Looijenga map, braid group. | | Source: | arXiv, math.DG/9903029 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No message found in this article forum.
You have a question or message about this article?
Ask the community and write a message in the forum.
If you want to rate this article, please use the review section..
To add a message in the forum, you need to login or register first. (free): registration page
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER