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On quadratic forms of 3-manifolds. (English) Zbl 0365.57001


MSC:

57N10 Topology of general \(3\)-manifolds (MSC2010)
11E16 General binary quadratic forms
15A63 Quadratic and bilinear forms, inner products
57Q35 Embeddings and immersions in PL-topology
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References:

[1] Blanchfield, R. C.: Intersection theory of manifolds with operators with applications to knot theory. Ann. of Math.65, 82-99 (1957) · Zbl 0080.16601 · doi:10.2307/1969966
[2] Crowell, R. H.: Corresponding group and module sequences. Nagoya math. J.19, 27-40 (1961) · Zbl 0101.26401
[3] Crowell, R. H., Fox, R. H.: Introduction to Knot Theory. Boston: Ginn and Co., 1963 · Zbl 0126.39105
[4] Erle, D.: Die quadratische Form eines Knotens und ein Satz über Knotenmannigfaltigkeiten. J. reine angew. Math. Band236, 174-218 (1969) · Zbl 0174.26503 · doi:10.1515/crll.1969.236.174
[5] Fox, R. H., Milnor, J. W.: Singularities of 2-spheres in 4-space and cobordism of knots. Osaka J. Math.3, 257-267 (1966) · Zbl 0146.45501
[6] Jaco, W.: Finitely presented subgroups of 3-manifold groups. Inventiones math.13, 335-346 (1971) · Zbl 0232.57003 · doi:10.1007/BF01406083
[7] Hosokawa, F.: OnV-polynomials of links. Osaka Math. J.,10, 273-282 (1958) · Zbl 0105.17404
[8] Jaco, W.: The structure of three-manifold groups. Mimeographed notes, Princeton Univ.
[9] Kawauchi, A.: Three dimensional homology handles and circles. Osaka J. Math.12, 565-581 (1975) · Zbl 0315.57002
[10] Kawauchi, A.: A partial Poincaré duality theorem for infinite cyclic coverings. Quart. J. Math.26, 437-458 (1975) · Zbl 0314.55008 · doi:10.1093/qmath/26.1.437
[11] Kawauchi, A.:H?-cobordism, part I. Osaka J. Math.13, 567-590 (1976) · Zbl 0358.55004
[12] Kawauchi, A.: A partial Poincaré duality theorem for topological infinite cyclic coverings and applications to higher dimensional topological knots (unpublished). A revised version will appear
[13] Levine, J.: Invariants of knot cobordism. Inventiones math.8, 98-110 (1969) · Zbl 0179.52401 · doi:10.1007/BF01404613
[14] Magnus, W., Karras, A., Solitar, D.: Combinatorial Group Theory. New York: Interscience 1966 · Zbl 0138.25604
[15] Matsumoto, Y.: Secondary intersectional properties of 4-manifolds and Whitney’s trick. To appear in Proceedings of Summer School (Stanford Univ. 1976) of A.M.S. · Zbl 0394.55010
[16] Milnor, J. W.: Infinite cyclic coverings. Conference on the Topology of Manifolds. Boston. Mass.: Prindle, Weber and Schmidt 1968 · Zbl 0179.52302
[17] Murasugi, K.: On a certain numerical invariant of link types. Trans. Amer. math. Soc.117, 387-422 (1967) · Zbl 0137.17903 · doi:10.1090/S0002-9947-1965-0171275-5
[18] Murasuga, K.: On the signature of links, Topology9, 283-298 (1970) · doi:10.1016/0040-9383(70)90018-2
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