Journal of the American Mathematical Society

Author(s): Richard Hain
Journal: J. Amer. Math. Soc. 10 (1997), 597-651.
MSC (1991): Primary 14G15, 57M99; Secondary 20F99
Retrieve article in: PDF
This article is available free of charge

1.: M. Asada, M. Kaneko: On the automorphism group of some pro- fundamental groups, in Galois Representations and Arithmetic Algebraic Geometry, editor Y. Ihara, Advanced Studies in Pure Mathematics 12 (1987), 137-159. MR 89h:20053
2.: M. Asada, H. Nakamura: On graded quotient modules of mapping class groups of surfaces, Israel J. Math. 90 (1995), 93-113. MR 96j:57015
3.: D. Bar-Natan: On the Vassiliev knot invariants, Topology 34 (1995), 423-472. MR 97d:57004
4.: G. Baumslag: On generalized free products, Math. Zeit. 78 (1962), 423-438. MR 25:3980
5.: J. Birman: Braids, Links, and Mapping Class Groups, Annals of Math. Studies 82, Princeton University Press, Princeton, 1975. MR 54:13894
6.: S. Bloch, I. Kriz: Mixed Tate Motives, Ann. of Math. 140 (1994), 557-605. MR 96c:11062
7.: A. Borel: Stable real cohomology of arithmetic groups, Ann. Sci. Ecole Norm. Sup. 7 (1974), 235-272. MR 52:8338
8.: A. Borel: Stable real cohomology of arithmetic groups II, Manifolds and Groups, Papers in Honor of Yozo Matsushima, Progress in Mathematics 14 , Birkhauser, Boston, 1981, 21-55. MR 83h:22023
9.: A. Borel: Private communication, November 1994.
10.: J. Carlson, R. Hain: Extensions of variations of mixed Hodge structure, Théorie de Hodge, Luminy, Juin 1987, Astérisque 179-180 (1989), 39-65. MR 91c:14016
11.: P. Cartier: Construction combinatoire des invariants de Vassiliev-Kontsevich des noeuds, C. R. Acad. Sci. Paris, t. 316, Série I (1993), 1205-1210. MR 94c:57004
12.: K.-T. Chen: Extension of $C^\infty$ function algebra and Malcev completion of $\pi _1$ , Adv. in Math. 23 (1977), 181-210.
13.: W. Fulton, J. Harris: Representation Theory, GTM 129, Springer-Verlag, 1991. MR 93a:20069
14.: R. Hain: The de Rham homotopy theory of complex algebraic varieties I, -Theory 1 (1987), 271-324. MR 88h:14029
15.: R. Hain: Algebraic cycles and extensions of variations of mixed Hodge structure, Proc. Symp. Pure Math. 53 (1991), 175-221. MR 92j:14008
16.: R. Hain: Letter to Looijenga, June 4, 1991.
17.: R. Hain: Completions of mapping class groups and the cycle , in Mapping Class Groups and Moduli Spaces of Riemann Surfaces, C.-F. Bödigheimer and R. Hain, editors, Contemp. Math. 150 (1993), 75-105. MR 95e:14018
18.: R. Hain: Torelli groups and Geometry of Moduli Spaces of Curves, in Current Topics in Complex Algebraic Geometry (C. H. Clemens and J. Kollar, eds.) MSRI publications no. 28, Cambridge University Press, 1995, 97-143. MR 97d:14036
19.: R. Hain: The Hodge de Rham Theory of Relative Malcev Completion, preprint, 1995.
20.: D. Johnson: An abelian quotient of the mapping class group ${\mathcal I}_g$ , Math. Ann. 249 (1980), 225-242. MR 87a:57008
21.: D. Johnson: The structure of the Torelli group I: A finite set of generators for ${\mathcal I}$ , Ann. of Math. 118 (1983), 423-442. MR 85a:57005
22.: D. Johnson: The structure of the Torelli group-III: The abelianization of ${\mathcal I}$ , Topology 24 (1985), 127-144. MR 87a:57016
23.: D. Johnson: A survey of the Torelli group, Contemp. Math. 20 (1983), 165-179. MR 85d:57009
24.: A. Kabanov: The second cohomology of moduli spaces of Riemann surfaces with twisted coefficients, Thesis, Duke University, 1995.
25.: A. Kabanov: The second cohomology with symplectic coefficients of the moduli space of smooth projective curves, Compositio Math., to appear.
26.: A. Kabanov: Stability of Schur functors, J. Algebra, to appear.
27.: C. Kassel: Quantum Groups, GTM 155, Springer-Verlag, 1995. MR 96e:17041
28.: T. Kohno: Série de Poincaré-Koszul associée aux groupes de tresses pures, Invent. Math. 82 (1985), 57-75. MR 87e:32015a
29.: T. Kohno: Monodromy representations of braid groups and Yang-Baxter equations, Ann. Inst. Fourier, Grenoble, 37 (1987), 139-160. MR 89h:17030
30.: T. Kohno, T. Oda: The lower central series of the pure braid group of an algebraic curve, in Galois Representations and Arithmetic Algebraic Geometry, editor: Y. Ihara, Advanced Studies in Pure Mathematics 12 (1987), 201-219. MR 90a:14026
31.: M. Kontsevich: Vassiliev's knot invariants, Advances in Soviet Math. 16, part 2 (1995), 137-150. MR 94k:57014
32.: J. Labute: On the descending central series of groups with a single defining relation, J. Algebra 14 (1970), 16-23. MR 40:4342
33.: A. Malcev: On a class of homogeneous spaces, Izv. Akad. Nauk SSSR Ser. Mat. 13 (1949), 9-32; English translation, Amer. Math.Soc. Transl. 39 (1962). MR 10:507e
34.: G. Mess: The Torelli groups for genus 2 and 3 surfaces, Topology 31 (1992), 775-790. MR 93k:57003
35.: J. Morgan: The algebraic topology of smooth algebraic varieties, Publ.Math. IHES 48 (1978), 137-204; correction, Publ. Math. IHES 64 (1986), 185. MR 80e:55020
36.: S. Morita: On the structure and the homology of the Torelli group, Proc. Japan Acad. 65 (1989), 147-150. MR 90h:57015
37.: S. Morita: Casson's invariant for homology 3-spheres and characteristic classes of surface bundles I, Topology 28 (1989), 305-323. MR 90h:57020
38.: S. Morita: On the structure of the Torelli group and the Casson invariant, Topology 30 (1991), 603-621. MR 92i:57016
39.: S. Morita: The extension of Johnson's homomorphism from the Torelli group to the mapping class group, Invent. Math. 111 (1993), 197-224. MR 93j:57001
40.: S. Morita: Abelian quotients of subgroups of the mapping class group of surfaces, Duke Math. Journal 70 (1993), 699-726. MR 94d:57003
41.: H. Nakamura, N. Takao, R. Ueno: Some stability properties of Teichmüller modular function fields with pro- weight structures, Math. Ann. 302 (1995), 197-213. MR 96h:14041
42.: K Nomizu: On the cohomology of compact homogeneous spaces of nilpotent Lie groups, Ann. of Math. 59 (1954), 167-189. MR 16:219e
43.: T. Oda: A lower bound for the weight graded quotients associated with the relative weight filtration on the Teichmüller group, preprint, 1992.
44.: D. Passman: The Algebraic Structure of Group Rings, John Wiley and Sons, New York, 1977. MR 81d:16001
45.: M. Pikaart: An orbifold partition of $\overline {M}^n_g$ , in The moduli space of curves, R. Dijkgraaf, C. Faber, G. van der Geer, editors, Birkhauser, 1995, 467-482. MR 96m:17002
46.: C. Reutenauer: Free Lie Algebras, Oxford University Press, 1993. MR 94j:17002
47.: M. Saito: Mixed Hodge modules and admissible variations, C. R. Acad.Sci. Paris, t. 309 (1989), Série I, 351-356. MR 91i:32029
48.: J.-P. Serre: Lie Algebras and Lie Groups, Benjamin, New York, 1965. MR 36:1582
49.: D. Sullivan: On the intersection ring of compact 3-manifolds, Topology 14 (1975), 275-277. MR 52:4296
50.: D. Sullivan: Infinitesimal computations in topology, Publ. Math. IHES 47 (1977), 269-331. MR 58:31119
51.: S. Zucker: Hodge theory with degenerating coefficients: cohomology in the Poincaré metric, Ann. of Math. 109 (1979), 415-476. MR 81a:14002

Retrieve articles in Journal of the American Mathematical Society with MSC (1991): 14G15, 57M99, 20F99

Richard Hain
Affiliation: Department of Mathematics, Duke University, Durham, North Carolina 27708-0320
Email: hain@math.duke.edu

DOI: 10.1090/S0894-0347-97-00235-X
PII: S 0894-0347(97)00235-X
Keywords: Mapping class groups, moduli spaces of curves, Malcev completion, Hodge theory
Received by editor(s): June 1, 1996
Received by editor(s) in revised form: February 3, 1997
Additional Notes: This work was supported in part by grants from the National Science Foundation.
Copyright of article: Copyright 1997, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN: 1088-6834(e) ISSN: 0894-0347(p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS