On the Birman invariants of Heegaard splittings
| dc.contributor.author | Montesinos Amilibia, José María | |
| dc.contributor.author | Safont Edo, Carmen | |
| dc.date.accessioned | 2023-06-20T17:03:37Z | |
| dc.date.available | 2023-06-20T17:03:37Z | |
| dc.date.issued | 1988-03 | |
| dc.description.abstract | 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. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/17092 | |
| dc.identifier.issn | 0030-8730 | |
| dc.identifier.officialurl | http://projecteuclid.org/euclid.pjm/1102689797 | |
| dc.identifier.relatedurl | http://pjm.math.berkeley.edu/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57704 | |
| dc.issue.number | 1 | |
| dc.journal.title | Pacific Journal of Mathematics | |
| dc.language.iso | eng | |
| dc.page.final | 142 | |
| dc.page.initial | 113 | |
| dc.publisher | Pacific Journal of Mathematics | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 515.163 | |
| dc.subject.keyword | 3-dimensional manifolds | |
| dc.subject.keyword | Heegaard splitting | |
| dc.subject.keyword | linking form | |
| dc.subject.ucm | Topología | |
| dc.subject.unesco | 1210 Topología | |
| dc.title | On the Birman invariants of Heegaard splittings | |
| dc.type | journal article | |
| dc.volume.number | 132 | |
| dcterms.references | 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. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 7097502e-a5b0-4b03-b547-bc67cda16ae2 | |
| relation.isAuthorOfPublication.latestForDiscovery | 7097502e-a5b0-4b03-b547-bc67cda16ae2 |
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