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Conjugacy relations in subgroups of the mapping class group and a group- theoretic description of the Rochlin invariant. (English) Zbl 0409.57010


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
57M10 Covering spaces and low-dimensional topology
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References:

[1] Artin, E.: Geometric algebra. New York: Interscience 1957 · Zbl 0077.02101
[2] Arf, C.: Untersuchungen über quadratische Formen in Körpern der Charakteristik 2. Crelles Math. J.183, 148-167 (1941) · Zbl 0025.01403
[3] Birman, J.: Braids, links, and mapping class groups. Annals of Mathematical Studies. Princeton: Princeton University Press 1975 · Zbl 0305.57013
[4] Birman, J.: group of homeomorphisms of a closed, oriented 2-manifold. Trans. Amer. Math. Soc.237, 283-309 (1978) · Zbl 0383.57006
[5] Johnson, D.: Homeomorphisms of a surface which act trivially on homology. Proc. Amer. Math. Soc.75, 119-125 (1979) · Zbl 0407.57003 · doi:10.1090/S0002-9939-1979-0529227-4
[6] Johnson, D.: Quadratic forms and the Birman-Craggs homomorphisms. Trans. Amer. Math. Soc. (to appear) · Zbl 0457.57006
[7] Johnson, D.: An abelian quotient of the mapping class groupI g . Math. Ann.249, 225-242 (1980) · Zbl 0428.57002 · doi:10.1007/BF01363897
[8] Lickorisch, W.B.R.: A representation of orientable combinatorial 3-manifolds. Ann. of Math.76, 531-540 (1962) · Zbl 0106.37102 · doi:10.2307/1970373
[9] Magnus, W., Karass, A., Solitar, D.: Combinatorial group theory. New York: Interscience 1966
[10] 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
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