Geodesic
Compactifications of moduli spaces and cellular decompositions
Zúñiga, Javier1
1Departamento de Economía, Universidad del Pacífico, Av Salaverry 2020, Jesús María, Lima, Peru
Algebraic and Geometric Topology, Tome 15 (2015) no. 1, pp. 1-41
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

This paper studies compactifications of moduli spaces involving closed Riemann surfaces. The first main result identifies the homeomorphism types of these compactifications. The second main result introduces orbicell decompositions on these spaces using semistable ribbon graphs extending the earlier work of Looijenga.

DOI : 10.2140/agt.2015.15.1
Classification : 32G15, 57M15, 30F30, 14H15
Keywords: moduli space, Riemann surfaces, ribbon graphs, fat graphs, orbicell decompositions

Zúñiga, Javier  1

1 Departamento de Economía, Universidad del Pacífico, Av Salaverry 2020, Jesús María, Lima, Peru 
@article{10_2140_agt_2015_15_1,
     author = {Z\'u\~niga, Javier},
     title = {Compactifications of moduli spaces and cellular decompositions},
     journal = {Algebraic and Geometric Topology},
     pages = {1--41},
     year = {2015},
     volume = {15},
     number = {1},
     doi = {10.2140/agt.2015.15.1},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2015.15.1/}
}
TY  - JOUR
AU  - Zúñiga, Javier
TI  - Compactifications of moduli spaces and cellular decompositions
JO  - Algebraic and Geometric Topology
PY  - 2015
SP  - 1
EP  - 41
VL  - 15
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2015.15.1/
DO  - 10.2140/agt.2015.15.1
ID  - 10_2140_agt_2015_15_1
ER  - 
%0 Journal Article
%A Zúñiga, Javier
%T Compactifications of moduli spaces and cellular decompositions
%J Algebraic and Geometric Topology
%D 2015
%P 1-41
%V 15
%N 1
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2015.15.1/
%R 10.2140/agt.2015.15.1
%F 10_2140_agt_2015_15_1
Zúñiga, Javier. Compactifications of moduli spaces and cellular decompositions. Algebraic and Geometric Topology, Tome 15 (2015) no. 1, pp. 1-41. doi: 10.2140/agt.2015.15.1

[1] B H Bowditch, D B A Epstein, Natural triangulations associated to a surface, Topology 27 (1988) 91

[2] K J Costello, The Gromov–Witten potential associated to a TCFT, (2005)

[3] K Costello, A dual version of the ribbon graph decomposition of moduli space, Geom. Topol. 11 (2007) 1637

[4] S L Devadoss, A space of cyclohedra, Discrete Comput. Geom. 29 (2003) 61

[5] S L Devadoss, T Heath, W Vipismakul, Deformations of bordered surfaces and convex polytopes, Notices Amer. Math. Soc. 58 (2011) 530

[6] J L Harer, The virtual cohomological dimension of the mapping class group of an orientable surface, Invent. Math. 84 (1986) 157

[7] E Harrelson, A Voronov, J Zúñiga, Open-closed moduli spaces and related algebraic structures, Lett. Math. Phys. 94 (2010) 1

[8] T Kimura, J Stasheff, A Voronov, Homology of moduli of curves and commutative homotopy algebras (editors I M Gelfand, J Lepowsky, M M Smirnov), Birkhäuser (1996) 151

[9] M Kontsevich, Intersection theory on the moduli space of curves and the matrix Airy function, Comm. Math. Phys. 147 (1992) 1

[10] C C M Liu, Moduli of J–holomorphic curves with Lagrangian boundary conditions and open Gromov–Witten invariants for an S1–equivariant pair, (2004)

[11] E Looijenga, Cellular decompositions of compactified moduli spaces of pointed curves, from: "The moduli space of curves" (editors R Dijkgraaf, C Faber, G van der Geer), Progr. Math. 129, Birkhäuser (1995) 369

[12] M Mulase, M Penkava, Ribbon graphs, quadratic differentials on Riemann surfaces, and algebraic curves defined over Q, Asian J. Math. 2 (1998) 875

[13] R C Penner, The decorated Teichmüller space of punctured surfaces, Comm. Math. Phys. 113 (1987) 299

[14] K Strebel, Quadratic differentials, 5, Springer, Berlin (1984)

[15] D Zvonkine, Strebel differentials on stable curves and Kontsevich’s proof of Witten’s conjecture, (2004)

Cité par Sources :