Biblioteca de la Universidad Complutense de Madrid

Surgery on double knots and symmetries

Impacto

Montesinos Amilibia, José María y Boileau, Michel y González Acuña, Francisco Javier (1987) Surgery on double knots and symmetries. Mathematische Annalen, 276 (2). pp. 323-340. ISSN 0025-5831

[img] PDF
Restringido a Sólo personal autorizado del repositorio hasta 31 Diciembre 2020.

1MB

URL Oficial: http://www.springerlink.com/content/g541h3376w7517jx/




Resumen

W. Whitten conjectured [Pacific J. Math. 97 (1981), no. 1, 209–216] that no 3-manifold obtained by a nontrivial surgery on a double of a noninvertible knot is a 2-fold branched covering of S3. The authors give counterexamples to this conjecture and determine the exact range of validity of the conjecture. More generally, they consider closed, orientable 3-manifolds obtained by nontrivial Dehn surgery on a double of a non-strongly invertible knot and study the symmetries of such manifolds, i.e. the homeomorphisms of finite order on these manifolds. They show that, except for a finite number of surgeries, these manifolds admit no (nontrivial) symmetry.


Tipo de documento:Artículo
Palabras clave:symmetries of 3-manifolds; Dehn surgeries on a double of a noninvertible knot; 2-fold branched covers of S 3
Materias:Ciencias > Matemáticas > Topología
Código ID:17172
Referencias:

Boileau, M., Siebenmann, L.: A planar classification of Pretzel knots and of Montesinos knots. Prepublication Orsay 1981

Bing, R., Martin, J.: Cubes with knotted holes. Trans. Am. Math. Soc.155, 217–231 (1971)

Bioleau, M.: Inversibilité des noeuds de Montesinos. Thèse de 3ème cycle (1979). Publication d'Orsay 1981

Boileau, M.: Variétés de dimension 3 et symétries des enrelacs. Thèse de doctorat (Université de Genève, 1985)

Bonnahon, F.: Involutions et fibrés de Seifert dans les variétés de dimension 3. Thèse de 3ème cycle, Orsay 1979

Bonahon, F., Siebenmann, L.: Algebraic knots. Monograph (to appear)

Bonahon, F., Siebenmann, L.: Seifert 3-orbifolds and their role as natural crystalline parts of arbitrary compact irreducible 3-orbiofolds. Preprint Orsay 1983

Boileau, M., Zimmermann, B.: Symmetries of sufficiently complicated Montesinos links. Preprint 1986

Burde, G., Zieschang, H.: Knots. Berlin, New York: de Gruyter 1985

Cannon, J.W., Feustel, C.D.: Essential embeddings of annuli and Möbius bands in 2-manifolds. Trans. Am. Math. Soc.215, 219–239 (1976)

Edmonds, A.L., Levingston, C.: Group actions on fibred 3-manifolds. Comment. Math. Helv.58, 529–542 (1983)

Freedman, M., Hass, J., Scott, P.: Least area incompressible surfaces in 3-manifolds. Invent. Math.71, 609–642 (1983)

Flapan, E.: Necessary and sufficient conditions for certain homology 3-spheres to have smoothZ p-actions. Pac. J. Math.117, 255–265 (1985)

Giffen, C.: On transformations of the 3-sphere fixing a knot. Bull. Am. Math. Soc.73, 913–914 (1967)

McA. Gordon, C., Litherland, R.: Incompressible surfaces in branched coverings. In: The Smith conjecture, p. 112. Morgan, J., Bass, H. (eds.) London, New York: Academic Press 1984

Gonzalez-Acuna, F.: Dehn's construction on knots. Bol. Soc. Mat. Mex. II. Ser.15, 58–79 (1970)

Hartley, R.: Knots with free period. Can. J. Math.,33, 91–102 (1981)

Hodgson, C.D.: Involutions and isotopies of lens spaces. Thesis, Melbourne 1981

Johannson, K.: Homotopy equivalence of 3-manifolds with boundaries. Lecture Notes Math. 761. Berlin, Heidelberrg, New York: Springer 1979

[JS] Jaco, W., Shalen, P.: Seifert fibred spaces in 3-manifolds. Memoirs A.M.S.220 (1979)

Kawauchi, A.: The invertibility problem of amphicherial excellent knots. Proc. Jap. Acad.55, 399–402 (1979)

Kim, P.K.: Involutions on Klein spacesM(p,q). Trans. Am. Math. Soc.268, 377–409 (1981)

Kojima, S.: Bounding finite group acting on 3-manifolds. Math. Proc. Camb. Phil. Soc.96, 269–284 (1984)

Meeks, W., Scott, P.: Finite group actions on 3-manifolds. Invent. Math.86, 287–346 (1986)

Meeks, W., Yau, S.T.: Topology of 3-dimensional manifolds and the embedding problem in minimal surface theory. Ann. Math.112, 481–484 (1980)

Montesinos, J.M.: Variedades de seifert que son recubridores ciclicos ramificados de dos hojas. Bol. Soc. Mat. Mex. II. Ser.18, 1–32 (1973)

Montesinos, J.M.: Revêtements doubles ramifiés de noeuds, variétés de Seifert et diagrmamme de Heegaard. Prépublication Orsay 1979

Montesinos, J.M.: Surgery on links and double branched covers ofS 3 in Knots, groups, and manifolds. Ann. Math. Stud.84, 227–259 (1975)

Montesinos, J.M., Whitten, W.: Constructions of two-fold branched coverings spaces. Preprint 1983

Myers, R.: Homology 3-spheres which admit no P.L. involutions. Pac. J. Math.94, 379–384 (1981)

Oertel, U.: Closed incompressible surfaces in complements of star links. Pac. J. Math.111, 209–230 (1984)

Schubert, H.: Knoten und Volringe. Acta Math.90, 132–286 (1953)

Seifert, H.: Topologie dreidimensionaler gefaserter Räume. Acta Math.60, 147–238 (1933)

Siebenmann, L.: On vanishing of the Rohlin invariant and non finitely amphicheiral homology 3-spheres. Proc. of Siegen Conference (1979). Lect. Notes Math.,788. Berlin, Heidelberg New York: Springer 1980

Bass, H., Morgan, J. (eds.): The Smith conjecture, 112. London, New York: Academic Press 1984

Thurston, W.P.: The geometry and topology of 3-manifolds. To be published by Princeton University Press

Tollefson, J.L.: Involution ofS 1×S 2 and other 3-manifolds. Trans. Am. Math. Soc.123, 223–234 (1976)

Tollefson, J.L.: Periodic homeomorphisms of 3-manifolds fibered overS 1. Trans. Am. Math. Soc.123, 223–234 (1976); Erratum, ibid. Tollefson, J.L.: Periodic homeomorphisms of 3-manifolds fibered overS 1. Trans. Am. Math. Soc.,243, 309–310 (1978)

Tollefson, J.L.: Involutions of seifert fiber spaces. Pac. J. Math.74, 519–529 (1978)

Trotter, H.F.: Non-invertible knots exist. Topology8, 275–280 (1964)

Waldhausen, F.: Über Involutionen der 3-Sphäre., Topology8, 81–91 (1969)

Waldhausen, F.: Eine Klasse von 3-dimensionalen Mannigfaltigkeiten, I and II. Invent. Math.3, 308–333 (1967);4, 87–117 (1967)

Waldhausen, F.: Gruppen mit Zentrum und 3-dimensionale Mannigfaltigkeiten. Topology6, 505–517 (1967)

Waldhausen, F.: On irreducible 3-manifolds which are sufficiently large. Ann. Math.87, 156–88 (1968)

Whitten, W.: Inverting double knots. Pac. J. Math.97, 209–216 (1981)

Zieschang, H.: Clasification of Montesinos knots. In: Topology, Proc. Leningrad 1983 (eds. L.D. Fadeev, A.A. Mal'cev) Lecture Notes Math. 1060, pp. 378–389. Berlin, Heidelberg, New York: Springer 1984

Zimmermann, B.: Das Nielsensche Realisierungsproblem für hinreichend große 3-Mannigfaltigkeiten. Math. Z.180, 349–359 (1982)

Depositado:22 Nov 2012 10:24
Última Modificación:07 Feb 2014 09:43

Sólo personal del repositorio: página de control del artículo