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On the Birman invariants of Heegaard splittings

Montesinos Amilibia, José María and Safont Edo, Carmen (1988) On the Birman invariants of Heegaard splittings. Pacific Journal of Mathematics, 132 (1). pp. 113-142. ISSN 0030-8730

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J. Birman had observed that the homological information about a given Heegaard splitting of genus g is contained in a double coset in the group of symplectic 2g×2g integer matrices with respect to a suitable subgroup, and found a determinant invariant of this double coset. We obtain complete invariants of these double cosets by characterizing it in terms of the linking form of the manifold lifted to a handlebody of the Heegaard splitting and then finding complete invariants of this lifted form.

Item Type:Article
Uncontrolled Keywords:3-dimensional manifolds; Heegaard splitting; linking form
Subjects:Sciences > Mathematics > Topology
ID Code:17092

H. Bass, K-heoryandstable algebra,PublicationsMathematiques IHES no. 22 (1964).

J. S. Birman, On the equivalence of Heegaard splittings of closed orientable 3-manifolds,Ann. Math. Studies, 84(1975), 137-139.

J. S. Birman, Lecture notes for the CBMS conference at Blacksburg, Va.,1977.

J.S.Birmanand D.Johnson, Homology Heegaardsplittings, manuscript.

J. S. Birman, F. Gonzalez-Acuna and J. Montesinos, Minimal Heegaard splittings of 3-manifolds are not unique, Michigan Math. J., 23 (1976),97-103.

J. S. Birman and H.Hilden, Heegaard splittings of branched coverings of S3, Trans. Amer. Math. Soc, 213 (1975),315-352.

F. Bonahon and S. P. Otal, Scindementsde Heegaarddes spaces lenticulares,C. R. Acad. Sci. Paris, 294 (1982),585-587.

E. Burger, Uber gruppen mit Verschlingungen, J. Reine Angew. Math., 188 (1950), 193-200.

D. Cooper, Signatures of surfaces in 3-manfolds and applications to knot and link cobordism, Ph.D., Warwick University (1982).

R. Engmann, Nicht homeomorphe Heegaard Zerlegungen von Geslecht 2 der Zusammenhngenden Summe zweier Linsenrame, Abh. Math. Sem. Univ. Hamburg, 35 (1970), 33-38.

C. Hodgson and J. H. Rubinstein, Involutions and Isotopies of Lens Spaces, Springer LNM #1144(1985).

A. Kawauchi and S. Kojima, Algebraic classification of linking pairings on 3-manifolds, Math. Ann.,253 (1980), 29-92.

J. Montesinos, Minimal plat representations of prime knots and links are not unique, Canad. J. Math., 28 (1976), 161-167.

J. Montesinos, Revetements doubles ramifies de noeuds, varietes de Seifert et diagrams de Heegaard, Polycopie Orsay (1979).

J. Montesinos and C. Safont, On the Birman invariants of Heegaard splittings, MSRI preprint #14102-85, November, 1985.

C. Safont, Ph.D. Thesis, University of Zaragoza, 1984.

H. Seifert, Verschlingungsinvarianten, Sitzumgsberichte der Preuss. Adad. der Wiss., Berlin, (1933),811-828.

H. Seifert-W. Threlfall, A Textbook of Topology,Academic Press, N.Y. (1980)

C. T. C. Wall, Quadratic forms onfinite groups, and related topics, Topology, 2 (1964),281-298.

F. Waldhausen, Heegaard Zerlegungen der 3-sphre, Topology, 7 (1968), 195-203.

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