Homology of origamis with symmetries

Carlos Matheus; Jean Christophe Yoccoz; David Zmiaikou

doi:10.5802/aif.2876

Homology of origamis with symmetries

Carlos Matheus
, Jean Christophe Yoccoz
, David Zmiaikou

Research output: Contribution to journal › Article › peer-review

Abstract

Given an origami (square-tiled surface) M with automorphism group Γ, we compute the decomposition of the first homology group of M into isotypic Γ-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.

Original language	English
Pages (from-to)	1131-1176
Number of pages	46
Journal	Annales de l'Institut Fourier
Volume	64
Issue number	3
DOIs	https://doi.org/10.5802/aif.2876
Publication status	Published - 1 Jan 2014
Externally published	Yes

Keywords

Affine group
Automorphisms group
Kontsevich-Zorich cocycle
Lyapunov exponents
Origamis
Regular and quasi-regular origamis
Representations of finite groups
Square-tiled surfaces

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10.5802/aif.2876

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title = "Homology of origamis with symmetries",

abstract = "Given an origami (square-tiled surface) M with automorphism group Γ, we compute the decomposition of the first homology group of M into isotypic Γ-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.",

keywords = "Affine group, Automorphisms group, Kontsevich-Zorich cocycle, Lyapunov exponents, Origamis, Regular and quasi-regular origamis, Representations of finite groups, Square-tiled surfaces",

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T1 - Homology of origamis with symmetries

AU - Matheus, Carlos

AU - Yoccoz, Jean Christophe

AU - Zmiaikou, David

PY - 2014/1/1

Y1 - 2014/1/1

N2 - Given an origami (square-tiled surface) M with automorphism group Γ, we compute the decomposition of the first homology group of M into isotypic Γ-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.

AB - Given an origami (square-tiled surface) M with automorphism group Γ, we compute the decomposition of the first homology group of M into isotypic Γ-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.

KW - Affine group

KW - Automorphisms group

KW - Kontsevich-Zorich cocycle

KW - Lyapunov exponents

KW - Origamis

KW - Regular and quasi-regular origamis

KW - Representations of finite groups

KW - Square-tiled surfaces

UR - https://www.scopus.com/pages/publications/84918820697

U2 - 10.5802/aif.2876

DO - 10.5802/aif.2876

M3 - Article

AN - SCOPUS:84918820697

SN - 0373-0956

VL - 64

SP - 1131

EP - 1176

JO - Annales de l'Institut Fourier

JF - Annales de l'Institut Fourier

IS - 3

ER -

Homology of origamis with symmetries

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Keywords

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