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Quadratic forms and the Birman-Craggs homomorphisms. (English) Zbl 0457.57006


MSC:

57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
57N10 Topology of general \(3\)-manifolds (MSC2010)
20F34 Fundamental groups and their automorphisms (group-theoretic aspects)
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[1] Cahit Arf, Untersuchungen über quadratische Formen in Körpern der Charakteristik 2. I, J. Reine Angew. Math. 183 (1941), 148 – 167 (German). · Zbl 0025.01403
[2] Joan S. Birman and R. Craggs, 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 (1978), 283 – 309. · Zbl 0383.57006
[3] Michael Freedman and Robion Kirby, A geometric proof of Rochlin’s theorem, Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976) Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc., Providence, R.I., 1978, pp. 85 – 97. · Zbl 0392.57018
[4] F. González-Acuña, Dehn’s construction on knots, Bol. Soc. Mat Mexicana (2) 15 (1970), 58 – 79. · Zbl 0229.55004
[5] C. McA. Gordon, Knots, homology spheres, and contractible 4-manifolds, Topology 14 (1975), 151 – 172. · Zbl 0304.57003
[6] John Milnor and Dale Husemoller, Symmetric bilinear forms, Springer-Verlag, New York-Heidelberg, 1973. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 73. · Zbl 0292.10016
[7] F. J. MacWilliams and N. J. A. Sloane, The theory of error-correcting codes, vol. 2, American Elsevier, New York, 1977. (See Chapter 13, Sections 2-5, particularly Theorems 4, 8, 12.) · Zbl 0369.94008
[8] Jerome Powell, Two theorems on the mapping class group of a surface, Proc. Amer. Math. Soc. 68 (1978), no. 3, 347 – 350. · Zbl 0391.57009
[9] Friedhelm Waldhausen, Heegaard-Zerlegungen der 3-Sphäre, Topology 7 (1968), 195 – 203 (German). · Zbl 0157.54501
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