Seifert fibred homology 3-spheres and the Yang-Mills equations on Riemann surfaces with marked points

Furuta, Mikio; Steer, B.

doi:10.1016/0001-8708(92)90051-l

Cited by 99 publications

(155 citation statements)

References 19 publications

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“…An Let Vectr denote the functor which assigns to any complex manifold S, the isomorphism classes of r-equivariant bundles E -X. The map E -E defines an isomorphism of functors, Vectr (X ) P arVect(X; Xl,' .. , Xb), [36], [23], [12], [10].…”

mentioning

confidence: 99%

Parabolic bundles, products of conjugacy classes, and Gromov-Witten invariants

Teleman¹,

Woodward²

2003

Annales De L’institut Fourier

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The set of conjugacy classes appearing in a product of conjugacy classes in a compact, 1-connected Lie group K can be identified with a convex polytope in the Weyl alcove [37]. In this paper we identify linear inequalities defining this polytope. Each inequality corresponds to a non-vanishing Gromov-Witten invariant for a generalized flag variety G/P , where G is the complexification of K and P is a maximal parabolic subgroup. This generalizes the results for SU (n) of Agnihotri and the second author [1] and Belkale [7] on the eigenvalues of a product of unitary matrices and quantum cohomology of Grassmannians.

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mentioning

confidence: 99%

Parabolic bundles, products of conjugacy classes, and Gromov-Witten invariants

Teleman¹,

Woodward²

2003

Annales De L’institut Fourier

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“…We can now apply Riemann-Roch-Kawasaki formula (see [20,29,7]) to the V -bundle W λ . It states that…”

Section: Torsion Function κ and The Riemann-roch-kawasaki Formulamentioning

confidence: 99%

“…endowed with a constant curvature metric; see e.g. [5] or [20 by isospectrality of P * P and P P * except on kernels. The only remaining term here has to be a constant, while we have a t −1/2 in (5.41).…”

Section: Annales De L'institut Fouriermentioning

confidence: 99%

Analytic torsions on contact manifolds

Rumin¹,

Seshadri²

2012

Ann. inst. Fourier

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We propose a definition for analytic torsion of the contact complex on contact manifolds. We show it coincides with Ray-Singer torsion on any 3-dimensional CR Seifert manifold equipped with a unitary representation. In this particular case we compute it and relate it to dynamical properties of the Reeb flow. In fact the whole spectral torsion function we consider may be interpreted on CR Seifert manifolds as a purely dynamical function through Selberg-type trace formulae.Comment: 40 page

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“…Let us briefly recall how to obtain this invariant (see for example [22] and [16] for a detailed construction). If x 1 , .…”

Section: 1mentioning

confidence: 99%

“…is an injection with image the set of tuples (c, [16]). In particular, if the N i 's are pairwise relatively prime, then…”

Section: That Ismentioning

confidence: 99%

Hearing the weights of weighted projective planes

Abreu¹,

Dryden

Freitas

et al. 2007

Ann Glob Anal Geom

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Abstract. Which properties of an orbifold can we "hear," i.e., which topological and geometric properties of an orbifold are determined by its Laplace spectrum? We consider this question for a class of four-dimensional Kähler orbifolds: weighted projective planes M := CP 2 (N 1 , N 2 , N 3 ) with three isolated singularities. We show that the spectra of the Laplacian acting on 0-and 1-forms on M determine the weights N 1 , N 2 , and N 3 . The proof involves analysis of the heat invariants using several techniques, including localization in equivariant cohomology. We show that we can replace knowledge of the spectrum on 1-forms by knowledge of the Euler characteristic and obtain the same result. Finally, after determining the values of N 1 , N 2 , and N 3 , we can hear whether M is endowed with an extremal Kähler metric.

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Seifert fibred homology 3-spheres and the Yang-Mills equations on Riemann surfaces with marked points

Cited by 99 publications

References 19 publications

Parabolic bundles, products of conjugacy classes, and Gromov-Witten invariants

Parabolic bundles, products of conjugacy classes, and Gromov-Witten invariants

Analytic torsions on contact manifolds

Hearing the weights of weighted projective planes

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