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Genus  mapping class groups are not Kähler
Author(s):
Razvan
Veliche
Journal:
Proc. Amer. Math. Soc.
135
(2007),
1441-1447.
MSC (2000):
Primary 32G15
Posted:
November 13, 2006
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Abstract:
The goal of this note is to prove that the mapping class groups of closed orientable surfaces of genus 2 (with punctures) are not Kähler. An application to compactifications of the moduli space of genus  curves (with punctures) is given.
References:
-
- [ABC:96]
- J. Amoros, M. Burger, K. Corlette, D. Kotschick, and D. Toledo.
Fundamental Groups of Compact Kähler Manifolds, volume 44 of Mathematical Surveys and Monographs.
American Mathematical Society, 1996. MR 1379330 (97d:32037) - [ABR92]
- D. Arapura, P. Bressler, and M. Ramachandran.
On the fundamental group of a compact kähler manifold.
Duke Math. J., 68(3):477-488, 1992. MR 1194951 (94e:57040) - [Bir75]
- Joan S. Birman.
Braids and Links and and Mapping Class Groups, volume 82 of Annals of Mathematics Studies.
Princeton University Press, 1975. MR 0375281 (51:11477) - [Cat03]
- Fabrizio Catanese.
Fibred Kähler and quasi-projective groups.
Adv. Geom. 2003, suppl., S13-S27.MR 2028385 (2004m:32034) - [Coh72]
- D.E. Cohen.
Groups of Cohomological Dimension One, volume 245 of Lecture Notes in Math.
Springer-Verlag, Berlin, 1972. MR 0344359 (49:9098) - [FL81]
- W. Fulton and R. Lazarsfeld.
Connectivity and its applications in algebraic geometry.
In Algebraic Geometry (Chicago, Ill., 1980), volume 862 of Lecture Notes in Math. Springer, Berlin, New York, 1981. MR 0644817 (83i:14002) - [GM83]
- M. Goresky and R. MacPherson.
Stratified Morse theory.
In Singularities, Part 1 (Arcata, Calif., 1981), volume 40 of Proc. Sympos. Pure Math. Amer. Math. Soc., Providence, R.I., 1983. MR 0713089 (84k:58017) - [Hai00]
- Richard Hain.
Moduli of Riemann surfaces, transcendental aspects.
In School on Algebraic Geometry (Trieste, 1999), volume 1 of ICTP Lect. Notes. Abdus Salam Int. Cent. Theoret. Phys., Trieste, 2000. MR 1795866 (2001m:32030) - [Hu59]
- Sze-Tsen Hu.
Homotopy Theory.
Academic Press, New York, 1959. MR 0106454 (21:5186) - [SW79]
- G.P. Scott and C.T.C. Wall.
Topological methods in group theory.
In Homological Group Theory, volume 36 of London Math. Soc. Lecture Note Ser. Cambridge Univ. Press, Cambridge, 1979. MR 0564422 (81m:57002)
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Additional Information:
Razvan
Veliche
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Address at time of publication:
Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
Email:
rveliche@math.utah.edu
DOI:
10.1090/S0002-9939-06-08636-9
PII:
S 0002-9939(06)08636-9
Received by editor(s):
February 25, 2005
Received by editor(s) in revised form:
December 16, 2005
Posted:
November 13, 2006
Dedicated:
To Oana and ``AAA''
Communicated by:
Michael Stillman
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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