On fiber-preserving isotopies of surface homeomorphisms

Fuller, Terry

doi:10.1090/S0002-9939-00-05642-2

On fiber-preserving isotopies of surface homeomorphisms
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Proc. Amer. Math. Soc. 129 (2001), 1247-1254 Request permission

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

Israel Berstein and Allan L. Edmonds, On the construction of branched coverings of low-dimensional manifolds, Trans. Amer. Math. Soc. 247 (1979), 87–124. MR 517687, DOI 10.1090/S0002-9947-1979-0517687-9
Joan S. Birman and Hugh M. Hilden, On isotopies of homeomorphisms of Riemann surfaces, Ann. of Math. (2) 97 (1973), 424–439. MR 325959, DOI 10.2307/1970830
T. Fuller, Hyperelliptic Lefschetz fibrations and branched covering spaces, to appear, Pacific J. Math.
R. Gompf and A. Stipsicz, An introduction to 4-manifolds and Kirby calculus, book in preparation.
Hugh M. Hilden, Three-fold branched coverings of $S^{3}$, Amer. J. Math. 98 (1976), no. 4, 989–997. MR 425968, DOI 10.2307/2374037
H. Hilden, personal communication.
A. Kas, On the handlebody decomposition associated to a Lefschetz fibration, Pacific J. Math. 89 (1980), no. 1, 89–104. MR 596919, DOI 10.2140/pjm.1980.89.89
José M. Montesinos, Three-manifolds as $3$-fold branched covers of $S^{3}$, Quart. J. Math. Oxford Ser. (2) 27 (1976), no. 105, 85–94. MR 394630, DOI 10.1093/qmath/27.1.85
José María Montesinos, $4$-manifolds, $3$-fold covering spaces and ribbons, Trans. Amer. Math. Soc. 245 (1978), 453–467. MR 511423, DOI 10.1090/S0002-9947-1978-0511423-7
B. Siebert and G. Tian, On hyperelliptic $C^{\infty }$-Lefschetz fibrations of four-manifolds, Commun. Contemp. Math. 1 (1999), 255–280.