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On the filtration of topological and pro-l mapping class groups of punctured Riemann surfaces
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1996 Volume 48 Issue 1 Pages 13-36
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- Published: 1996 Received: February 14, 1994 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Correction information
Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : An) M. P. Anderson, Exactness properties of profinite completion functors, Topology, 13 (1974), 229-239.
Ar) E. Artin, Geometric Algebra, Interscience, New York, 1957.
As) M. Asada, Two properties of the filtration of the outer automorphism groups of certain groups, Math. Z., 218 (1995), 123-133.
AK) M. Asada and M. Kaneko, On the automorphism group of some pro-l fundamental groups, In Galois Representations and Arithmetic Algebraic Geometry, (ed. Y. Ihara), Adv. Stud. Pure Math., 12 (1987), 137-159.
AMO) M. Asada, M. Matsumoto and T. Oda, Local monodromy on the fundamental groups of algebraic curves along a degenerate stable curve, to appear in J. Pure Appl. Algebra.
AN) M. Asada and H. Nakamura, On graded quotient modules of mapping class groups of surfaces, Israel J. Math., 90 (1995), 93-113.
BL) H. Bass and A. Lubotzky, Linear-central filtrations on groups, Contemp. Math., 169 (1994), 45-98.
Bi1) J. S. Birman, Mapping class groups and their relationship to braid groups, Comm. Pure Appl. Math., 22 (1969), 213-238.
Bi2) J. S. Birman, Braids, Links and Mapping Class Groups, Ann. of Math. Stud., 82, Princeton Univ. Press, 1975.
Bi3) J. S. Birman, The algebraic structure of surface mapping class groups, In Discrete Groups and Automorphic Functions, (ed. W. Harvey), Academic Press, New York, 1977.
Bl) S. Bloch, A letter to P. Deligne, 1984.
Bo) N. Bourbaki, Groupes et algèbres de Lie, Chapitres 2 et 3, Hermann, Paris, 1972.
I) Y. Ihara, Automorphisms of pure sphere braid groups and Galois representations, In The Grothendieck Festshrift, Vol. 2, Birkhäuser, Boston, 1990.
IK) Y. Ihara and M. Kaneko, Pro-l pure braid groups of Riemann surfaces and Galois representations, Osaka J. Math., 29 (1992), 1-19.
J) D. Johnson, An abelian quotient of the mapping class group Ig, Math. Ann., 249 (1980), 225-242.
k) M. Kaneko, Certain automorphism groups of pro-l fundamental groups of punctured Riemann surfaces, J. Fac. Sci. Univ. Tokyo, 36 (1989), 363-372.
La) J. Labute, On the descending central series of groups with a single defining relation, J. Algebra, 14 (1970), 16-23.
Lu) A. Lubotzky, Combinatorial group theory for pro-p groups, J. Pure Appl. Algebra, 25 (1982), 311-325.
MKS) W. Magnus, A. Karrass and D. Solitar, Combinatorial Group Theory, Interscience Publ. Wiley and Sons, 1966.
M1) S. Morita, Casson's invariant for homology 3-spheres and characteristic classes of surface bundles I, Topology, 28 (1989), 305-323.
M2) S. Morita, Abelian quotients of subgroups of the mapping class group of surfaces, Duke Math. J., 70 (1993), 699-726.
N) H. Nakamura, On exterior Galois representations associated with open elliptic curves, J. Math. Sci. Univ. Tokyo, 2 (1995), 197-231.
NT) H. Nakamura and H. Tsunogai, Some finiteness theorems on Galois centralizers in pro-l mapping class groups, J. Reine Angew. Math., 441 (1993), 115-144.
O1) T. Oda, Galois action on the pro-nilpotent completion of the fundamental groups of algebraic curves, (in Japanese), In Algebraic Analysis and Number Theory, RIMS report, 810 (1992), 318-323.
O2) T. Oda, A lower bound for the graded modules associated with the relative weight filtration on the Teichmüller group, preprint, 1992.
Se1) J.-P. Serre, Rigidité du foncteur de Jacobi d'échelon n_??_3, Appendice à l'exposé 17 du Séminaire Cartan, 1960-1961.
Se2) J.-P. Serre, Groupes de congruence, (d'après H. Bass, H. Matsumoto, J. Mennicke, J. Milnor, C. Moore), Séminaire Bourbaki, 1966/67, 330.
Sh) G. Shimura, Arithmetic of alternating forms and quaternion hermitian forms, J. Math. Soc. Japan, 15 (1963), 33-65.
Wa) R. B. Warfield, Nilpotent groups, Lecture Notes in Math., 513, Springer, Berlin-Heidelberg-New York, 1976.
Wi) E. Witt, Treue Darstellung Liescher Ringe, J. Reine Angew. Math., 177 (1937), 152-160.
Right : [An] M. P. Anderson, Exactness properties of profinite completion functors, Topology, 13 (1974), 229-239.
[Ar] E. Artin, Geometric Algebra, Interscience, New York, 1957.
[As] M. Asada, Two properties of the filtration of the outer automorphism groups of certain groups, Math. Z., 218 (1995), 123-133.
[AK] M. Asada and M. Kaneko, On the automorphism group of some pro-l fundamental groups, In Galois Representations and Arithmetic Algebraic Geometry, (ed. Y. Ihara), Adv. Stud. Pure Math., 12 (1987), 137-159.
[AMO] M. Asada, M. Matsumoto and T. Oda, Local monodromy on the fundamental groups of algebraic curves along a degenerate stable curve, to appear in J. Pure Appl. Algebra.
[AN] M. Asada and H. Nakamura, On graded quotient modules of mapping class groups of surfaces, Israel J. Math., 90 (1995), 93-113.
[BL] H. Bass and A. Lubotzky, Linear-central filtrations on groups, Contemp. Math., 169 (1994), 45-98.
[Bi1] J. S. Birman, Mapping class groups and their relationship to braid groups, Comm. Pure Appl. Math., 22 (1969), 213-238.
[Bi2] J. S. Birman, Braids, Links and Mapping Class Groups, Ann. of Math. Stud., 82, Princeton Univ. Press, 1975.
[Bi3] J. S. Birman, The algebraic structure of surface mapping class groups, In Discrete Groups and Automorphic Functions, (ed. W. Harvey), Academic Press, New York, 1977.
[Bl] S. Bloch, A letter to P. Deligne, 1984.
[Bo] N. Bourbaki, Groupes et algèbres de Lie, Chapitres 2 et 3, Hermann, Paris, 1972.
[I] Y. Ihara, Automorphisms of pure sphere braid groups and Galois representations, In The Grothendieck Festshrift, Vol. 2, Birkhäuser, Boston, 1990.
[IK] Y. Ihara and M. Kaneko, Pro-l pure braid groups of Riemann surfaces and Galois representations, Osaka J. Math., 29 (1992), 1-19.
[J] D. Johnson, An abelian quotient of the mapping class group Ig, Math. Ann., 249 (1980), 225-242.
[k] M. Kaneko, Certain automorphism groups of pro-l fundamental groups of punctured Riemann surfaces, J. Fac. Sci. Univ. Tokyo, 36 (1989), 363-372.
[La] J. Labute, On the descending central series of groups with a single defining relation, J. Algebra, 14 (1970), 16-23.
[Lu] A. Lubotzky, Combinatorial group theory for pro-p groups, J. Pure Appl. Algebra, 25 (1982), 311-325.
[MKS] W. Magnus, A. Karrass and D. Solitar, Combinatorial Group Theory, Interscience Publ. Wiley and Sons, 1966.
[M1] S. Morita, Casson's invariant for homology 3-spheres and characteristic classes of surface bundles I, Topology, 28 (1989), 305-323.
[M2] S. Morita, Abelian quotients of subgroups of the mapping class group of surfaces, Duke Math. J., 70 (1993), 699-726.
[N] H. Nakamura, On exterior Galois representations associated with open elliptic curves, J. Math. Sci. Univ. Tokyo, 2 (1995), 197-231.
[NT] H. Nakamura and H. Tsunogai, Some finiteness theorems on Galois centralizers in pro-l mapping class groups, J. Reine Angew. Math., 441 (1993), 115-144.
[O1] T. Oda, Galois action on the pro-nilpotent completion of the fundamental groups of algebraic curves, (in Japanese), In Algebraic Analysis and Number Theory, RIMS report, 810 (1992), 318-323.
[O2] T. Oda, A lower bound for the graded modules associated with the relative weight filtration on the Teichmüller group, preprint, 1992.
[Se1] J. -P. Serre, Rigidité du foncteur de Jacobi d'échelon n≥3, Appendice à l'exposé 17 du Séminaire Cartan, 1960-1961.
[Se2] J. -P. Serre, Groupes de congruence, (d'après H. Bass, H. Matsumoto, J. Mennicke, J. Milnor, C. Moore), Séminaire Bourbaki, 1966/67, 330.
[Sh] G. Shimura, Arithmetic of alternating forms and quaternion hermitian forms, J. Math. Soc. Japan, 15 (1963), 33-65.
[Wa] R. B. Warfield, Nilpotent groups, Lecture Notes in Math., 513, Springer, Berlin-Heidelberg-New York, 1976.
[Wi] E. Witt, Treue Darstellung Liescher Ringe, J. Reine Angew. Math., 177 (1937), 152-160.
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