×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI EuDML
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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.