The structure and singularities of quotient arc complexes

Journal of Topology

Volumn 1, Issue 3, 2008, Pages 527-550

  Penner, R C ^a,b  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

^b AARHUS UNIVERSITY   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 55049085382     PISSN: 17538416     EISSN: 17538424     Source Type: Journal    
DOI: 10.1112/jtopol/jtn006     Document Type: Article

References (26)

1. A. Borel, Seminar on transformation groups, 1960, Princeton, NJ, Princeton University Press, Annals of Mathematics Studies 46
2. B. Bowditch, D. B. A. Epstein, Natural triangulations associated to a surface, Topology, 1988, 27, 91–117
3. A. Fathi, F. Laudenbach, V. Poenaru, Travaux de Thurston sur les surfaces, Astérisque 66–67 (Soc. Math. de France, Paris, 1979)
4. J. L. Harer, Stability of the homology of the mapping class groups of orientable surfaces, Ann. of Math., 1985, 121, 215–249
5. J. L. Harer, The virtual cohomological dimension of the mapping class group of an orientable surface, Invent. Math., 1986, 84, 157–176
6. J. L. Harer, D. Zagier, The Euler characteristic of the moduli space of curves, Invent. Math., 1986, 85, 457–485
7. W. J. Harvey, Boundary structure of the modular group, Riemann surfaces and related topics, Proceedings of the 1978 Stony Brook Conference, Annals of Mathematics Studies 97 (Princeton University Press, Princeton, NJ, 1981) 245–251
8. A. Hatcher, Algebraic topology, www.math.cornell.edu/hatcher/AT/ATpage.html
9. J. H. Hubbard, H. Masur, Quadratic differentials and foliations, Acta Math., 1979, 142, 221–274
10. K. Igusa, Combinatorial Miller–Morita–Mumford classes and Witten cycles, Algebr. Geom. Topol., 2004, 4, 473–520
11. N. Ivanov, Stabilization of the homology of Teichmüller modular groups, Algebra i Analiz, 1989, 1, 110–126, (Russian); Leningrad Math. J. 1 (1990) 675–691 (English)
12. N. Ivanov, On the homology stability for Teichmüller modular groups: closed surfaces and twisted coefficients, Mapping class groups and moduli spaces of Riemann surfaces, Göttingen, 1991/Seattle, WA, 1991, Contemporary Mathematics 150 (American Mathematical Society, Providence, RI, 1993) 149–194
13. W. H. Jaco, P. B. Shalen, Seifert fibered spaces in three manifolds, Mem. Amer. Math. Soc., 1979, 21, 220
14. M. Kontsevich, Intersection theory on the moduli space of curves and the matrix Airy function, Comm. Math. Phys., 1992, 147, 1–23
15. E. Looijenga, R. Dijgraaf, C. Faber, G. van der Geer, Cellular decompositions of compactified moduli spaces of pointed curves, The moduli space of curves, 1995, Birkhäuser, Boston, 369–400
16. J. Milnor, Lectures on the h-cobordism theorem, Notes by L. Siebenmann and J. Sondow (Princeton University Press, Princeton, NJ, 1965)
17. M¯g,n are tautological, Int. Math. Res. Not., 2004, 2329–2390
18. R. C. Penner, The action of the mapping class group on curves and arcs in surfaces, Thesis, Massachusetts Institute of Technology, 1982
19. R. C. Penner, The decorated Teichmüller space of punctured surfaces, Comm. Math. Phys., 1987, 113, 299–339
20. R. C. Penner, Perturbative series and the moduli space of Riemann surfaces, J. Differential Geom., 1988, 27, 35–53
21. R. C. Penner, Weil–Petersson volumes, J. Differential Geom., 1992, 35, 559–608
22. R. C. Penner, The simplicial compactification of Riemann's moduli space, Proceedings of the 37th Taniguchi Symposium, 1996, World Scientific, 237–252
23. R. C. Penner, Decorated Teichmüller theory of bordered surfaces, Comm. Anal. Geom., 2004, 12, 793–820
24. R. C. Penner, J. L. Harer, Combinatorics of train tracks, 1992, Princeton, NJ, Princeton University Press, Annals of Mathematics Studies 125
25. C. P. Rourke, B. J. Sanderson, Introduction to piecewise-linear topology, 1972, Berlin, Springer, Ergebnisse der Mathematik und ihrer Grenzgebiete 69
26. K. Strebel, Quadratic differentials, 1984, Berlin, Springer, Ergebnisse der Mathematik und ihrer Grenzgebiete