Teichmüller theory for surfaces with boundary

Earle, Clifford J.; Schatz, Alfred H.

doi:10.4310/jdg/1214429381

Cited by 98 publications

(98 citation statements)

References 10 publications

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“…is also a homotopy equivalence: Earle and Schatz result [21] extends to a nonconnected surface F if each component has at least one boundary component. Therefore we have partially recovered the following proposition:…”

Section: The Props Isomorphismmentioning

confidence: 99%

“…, is equal to the inverse of ρ in * , ρ a), is the generator of the mapping class group Γ 0,1+1 = π 0 (Dif f + (C, ∂)) ∼ = Z. By [21], the morphism of groups σ : Z ≈ → Dif f + (C, ∂) sending n ∈ Z to the n-th composite D n of D, is a homotopy equivalence. By applying the classifying construction, we obtain the map that we denoted before B(σ).…”

Section: Lemma 55 the Morphism Of Left H * (G)-modulesmentioning

confidence: 99%

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String topology of classifying spaces

Chataur

Menichi

2012

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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Abstract. Let G be a finite group or a compact connected Lie group and let BG be its classifying space. Let LBG := map(S 1 , BG) be the free loop space of BG i.e. the space of continuous maps from the circle S 1 to BG. The purpose of this paper is to study the singular homology H * (LBG) of this loop space. We prove that when taken with coefficients in a field the homology of LBG is a homological conformal field theory. As a byproduct of our main theorem, we get a Batalin-Vilkovisky algebra structure on the cohomology H * (LBG). We also prove an algebraic version of this result by showing that the Hochschild cohomology HH

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Section: The Props Isomorphismmentioning

confidence: 99%

Section: Lemma 55 the Morphism Of Left H * (G)-modulesmentioning

confidence: 99%

String topology of classifying spaces

Chataur

Menichi

2012

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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“…The projection from H (F ) to T (F ) is a principal Diff 1 -bundle [7], [8]. Since H (F ) is contractible and T (F ) ∼ = R 6g−6+2b , the subgroup Diff 1 (F ) must be contractible.…”

Section: Application Of Vassilievmentioning

confidence: 99%

The stable moduli space of Riemann surfaces: Mumford’s conjecture

2007

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D. Mumford conjectured in [33] that the rational cohomology of the stable moduli space of Riemann surfaces is a polynomial algebra generated by certain classes κ i of dimension 2i. For the purpose of calculating rational cohomology, one may replace the stable moduli space of Riemann surfaces by BΓ ∞ , where Γ ∞ is the group of isotopy classes of automorphisms of a smooth oriented connected surface of "large" genus. Tillmann's theorem [44]

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“…(For the sake of brevity we do not state their results for nonorientable surfaces or surfaces with boundary, cf. Earle and Schatz [28].) The result for/?…”

Section: If (I(z) Is a Measurable Function Defined For All Z E C And mentioning

confidence: 99%

Quasiconformal mappings, with applications to differential equations, function theory and topology

Bers¹

1977

Bull. Amer. Math. Soc.

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The theory of quasiconformal mappings is nearly 50 years old (see [44] for references to the papers by Grötzsch, Ahlfors Lavrent'ev and Morrey from the 20's and 30's) and the interest in them does not seem to wane. These mappings may be studied for their own sake or as a tool for attacking other mathematical problems; they are indeed a powerful and flexible tool. The purpose of this lecture is to state two basic theorems about quasiconformal mappings in two dimensions (the existence theorem, the first version of which is due to Gauss, and Teichmüller's theorem about extremal quasiconformal mappings) and to discuss some applications of these theorems. The discussion will necessarily be sketchy and several important topics will be slighted or not even mentioned. We begin by defining the concept of quasiconformality.

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Teichmüller theory for surfaces with boundary

Cited by 98 publications

References 10 publications

String topology of classifying spaces

String topology of classifying spaces

The stable moduli space of Riemann surfaces: Mumford’s conjecture

Quasiconformal mappings, with applications to differential equations, function theory and topology

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