Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On fiber-preserving isotopies of surface homeomorphisms

Author: Terry Fuller
Journal: Proc. Amer. Math. Soc. 129 (2001), 1247-1254
MSC (1991): Primary 57M12
Published electronically: October 11, 2000
MathSciNet review: 1709751
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that there are homeomorphisms of closed oriented genus $g$ surfaces $\Sigma_g$ which are fiber-preserving with respect to an irregular branched covering $\Sigma_g \to S^2$ and isotopic to the identity, but which are not fiber-isotopic to the identity.

References [Enhancements On Off] (What's this?)

  • [1] I. Berstein and A. Edmonds, On the construction of branched coverings of low-dimensional manifolds, Trans. Amer. Math. Soc. 247 (1979), 87-124. MR 80b:57003
  • [2] J. Birman, H. Hilden, On isotopies of homeomorphisms of Riemann surfaces, Ann. of Math. 97 (1973), 424-439. MR 48:4305
  • [3] T. Fuller, Hyperelliptic Lefschetz fibrations and branched covering spaces, to appear, Pacific J. Math.
  • [4] R. Gompf and A. Stipsicz, An introduction to 4-manifolds and Kirby calculus, book in preparation.
  • [5] H. Hilden, Three-fold branched coverings of $S^3$, Amer. J. Math. 98 (1976), 989-997. MR 54:13917
  • [6] H. Hilden, personal communication.
  • [7] A. Kas, On the handlebody decomposition associated to a Lefschetz fibration, Pacific J. Math. 89 (1980), 89-104. MR 82f:57012
  • [8] J. M. Montesinos, Three-manifolds as 3-fold branched covers of $S^3$, Quart. J. Math. Oxford Ser. (2) 27 (1976), 85-94. MR 52:15431
  • [9] J. M. Montesinos, 4-manifolds, 3-fold coverings, and ribbons, Trans. Amer. Math. Soc. 245 (1978), 453-467. MR 80k:57001
  • [10] B. Siebert and G. Tian, On hyperelliptic $C^{\infty}$-Lefschetz fibrations of four-manifolds, Commun. Contemp. Math. 1 (1999), 255-280. CMP 99:14

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 57M12

Retrieve articles in all journals with MSC (1991): 57M12

Additional Information

Terry Fuller
Affiliation: School of Mathematics, Institute for Advanced Study, Olden Lane, Princeton, New Jersey 08540
Address at time of publication: Department of Mathematics, California State University, Northridge, California 91330

Received by editor(s): June 16, 1999
Received by editor(s) in revised form: July 7, 1999
Published electronically: October 11, 2000
Additional Notes: The author was supported by NSF grant DMS 97-29992.
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society