HOMOLOGY OF ORIGAMIS WITH SYMMETRIES

被引：9

作者：

Matheus, Carlos ^{[1
]}

Yoccoz, Jean-Christophe ^{[2
]}

Zmiaikou, David ^{[3
]}

机构：

[1] Univ Paris 13, Sorbonne Paris Cite, LAGA, CNRS,UMR 7539, F-93430 Villetaneuse, France

[2] Coll France PSL, F-75005 Paris, France

[3] Univ Paris 11, Dept Math, F-91405 Orsay, France

来源：

ANNALES DE L INSTITUT FOURIER | 2014年 / 64卷 / 03期

关键词：

Origamis; square-tiled surfaces; automorphisms group; affine group; representations of finite groups; regular and quasi-regular origamis; Kontsevich-Zorich cocycle; Lyapunov exponents; TEICHMULLER CURVES; LYAPUNOV; TRANSFORMATIONS; DEVIATION; SURFACES; SPACE;

D O I：

10.5802/aif.2876

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given an origami (square-tiled surface) M with automorphism group Gamma, we compute the decomposition of the first homology group of M into isotypic Gamma-submodules. Through the action of the affine group of M on the homology group, we deduce some consequences for the multiplicities of the Lyapunov exponents of the Kontsevich-Zorich cocycle. We also construct and study several families of interesting origamis illustrating our results.

引用

页码：1131 / 1176

页数：46

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