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An abelian quotient of the mapping class group \(\mathfrak S\). (English) Zbl 0409.57009


MSC:

57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
20F34 Fundamental groups and their automorphisms (group-theoretic aspects)
57M05 Fundamental group, presentations, free differential calculus
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References:

[1] Birman, J.:Braids, links, and mapping class groups. Annals of Math. Studies No. 82. Princeton: Princeton Univ. Press 1975 · Zbl 0305.57013
[2] Birman, J., Craggs, R.: The ?-invariant of 3-manifolds and certain structural properties of the group of Homeomorphisms of a closed, oriented 2-manifold. Trans. Amer. Math. Soc.237, 283-309 (1978) · Zbl 0383.57006
[3] Chillingworth, D.R.J.: Winding numbers on surfaces. I. Math. Ann.196, 218-249 (1972) · Zbl 0227.57001 · doi:10.1007/BF01428050
[4] Chillingworth, D.R.J.: Winding numbers on surfaces. II. Math. Ann.199, 131-153 (1972) · Zbl 0238.57001 · doi:10.1007/BF01431419
[5] Johnson, D.: Homeomorphisms of a surface which act trivially on homology. Proc. AMS75, 119-125 (1979) · Zbl 0407.57003 · doi:10.1090/S0002-9939-1979-0529227-4
[6] Johnson, D.: Quadratic forms and the Birman-Craggs homomorphisms. Amer. Math. Soc. (to appear) · Zbl 0457.57006
[7] Milnor, J.: Introduction to AlgebraicK-theory. Annals of Math. Studies No. 72. Princeton: Princeton Univ. Press 1971 · Zbl 0237.18005
[8] Magnus, W., Karass, A., Solitar, D.: Combinatorial group theory. New York: Interscience 1966
[9] Powell, J.: Two theorems on the mapping class group of surfaces. Proc. Amer. Math. Soc.68, 347-350 (1978) · Zbl 0391.57009 · doi:10.1090/S0002-9939-1978-0494115-8
[10] Reinhart, B.L.: The winding number on 2-manifolds. Ann. Inst. Fourier (Grenoble)10, 271-283 (1960) · Zbl 0097.16203
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