Roots of the canonical bundle of the universal Teichm�ller curve and certain subgroups of the mapping class group

Sipe, Patricia L.

doi:10.1007/bf01475756

Cited by 22 publications

(41 citation statements)

References 10 publications

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“…Interesting results on invariant r-roots can be found in [15] (a "square root" being a spin structure). A growing number of references on invariant spin structures have to do with mapping class groups and moduli spaces of spin curves.…”

Section: Introductionmentioning

confidence: 99%

Invariant Spin Structures on Riemann Surfaces

Kallel¹,

Sjerve²

2011

Annales De La Faculté Des Sciences De Toulouse : Mathématiques

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Section: Introductionmentioning

confidence: 99%

Invariant Spin Structures on Riemann Surfaces

Kallel¹,

Sjerve²

2011

Annales De La Faculté Des Sciences De Toulouse : Mathématiques

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“…Since Teichmüller spaces are contractible, the Teichmüller curves are topologically trivial fibrations. At times (see for example [12]), smooth trivializations are useful. Our purpose here is to present explicit real analytic trivializations.…”

Section: Introductionmentioning

confidence: 99%

Some explicit real analytic trivializations of the Teichmüller curves

Earle¹

1988

Proc. Amer. Math. Soc.

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ABSTRACT. The barycentric extension of homeomorphisms from the unit circle to the closed unit disk produces real analytic trivializations of the Teichmüller curves.1. Introduction.In part because of their universal properties (see [5, 6, and 9]) the Teichmüller curves have played a central role in the deformation theory of Riemann surfaces. Since Teichmüller spaces are contractible, the Teichmüller curves are topologically trivial fibrations. At times (see for example [12]), smooth trivializations are useful. Our purpose here is to present explicit real analytic trivializations. These trivializations, which we obtain from the barycentric extension introduced by Douady and the author in [3], have invariance properties that may be useful. We present our basic construction in the next section. The final section describes the resulting trivializations.We assume some familiarity with the Ahlfors-Bers theory of Teichmüller spaces. Facts for which no reference is given can be found in the recent books [8, 10, or

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“…In [8,9], the author studied an action of the Teichmüller modular group on the nth roots of the canonical bundle of the universal Teichmüller curve (n is an integer dividing 2p -2). Topological descriptions of the nth roots and the action were given, and the subgroups GPin of the modular group Modp which fix all nth roots were characterized (these results are summarized here in §2).…”

Section: Introductionmentioning

confidence: 99%

Some finite quotients of the mapping class group of a surface

Sipe¹

1986

Proc. Amer. Math. Soc.

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ABSTRACT. Let S be a smooth, oriented, compact surface of genus p > 2, and Modp its Teichmüller modular group (or mapping class group). Let T\ (S) denote the unit tangent bundle, and let n be an integer dividing 2p -2. Modp acts on the finite set '5n, the elements of which are certain homomorphisms from Hi(Tx(S),Zn)to Zn-In previous work of the author, these homomorphisms arose as the topological description of the nth roots of the canonical bundle of the universal Teichmüller curve; however, a topological approach is taken here. The subgroups of Gp,n which leave all elements of 5>n fixed are subgroups of finite index in Modp. Let Qn = Modp/Gp,n.The elements of Qn are characterized algebraically. Qn is an extension of (2Zn)2p by the symplectic group Sp(p, Zn) (and in the case of n odd, Qn is a semidirect product).

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Roots of the canonical bundle of the universal Teichm�ller curve and certain subgroups of the mapping class group

Cited by 22 publications

References 10 publications

Invariant Spin Structures on Riemann Surfaces

Invariant Spin Structures on Riemann Surfaces

Some explicit real analytic trivializations of the Teichmüller curves

Some finite quotients of the mapping class group of a surface

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