On the Imbedding of V-Manifolds in Projective Space

Baily, Walter L.

doi:10.2307/2372689

Cited by 86 publications

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“…f : M → BU (d). Construction of such a map for the case of orbifolds has been developed by Baily [33] and, in particular, forM g,n by Wolpert [29]. The n-vector complex bundle λ over the base space M can be expressed as a pullback of the standard vector bundle ξ over BU (d) .…”

Section: From Chern Classes To Grassmanniansmentioning

confidence: 99%

Kontsevich–Witten model from 2+1 gravity: new exact combinatorial solution

Kholodenko¹

2002

Journal of Geometry and Physics

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In previous publications ( J. Geom. Phys.38 (2001) 81-139 and references therein ) the partition function for 2+1 gravity was constructed for the fixed genus Riemann surface.With help of this function the dynamical transition from pseudo-Anosov to periodic (Seifert-fibered) regime was studied. In this paper the periodic regime is studied in some detail in order to recover major results of Kontsevich (Comm.Math.Phys. 147 (1992) 1-23 ) inspired by earlier work of Witten on topological two dimensional quantum gravity.To achieve this goal some results from enumerative combinatorics have been used. The logical developments are extensively illustrated using geometrically convincing figures. This feature is helpful for development of some non traditional applications (mentioned through the entire text) of obtained results to fields other than theoretical particle physics.

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Section: From Chern Classes To Grassmanniansmentioning

confidence: 99%

Kontsevich–Witten model from 2+1 gravity: new exact combinatorial solution

Kholodenko¹

2002

Journal of Geometry and Physics

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“…Since the orbifold Z is Kähler-Einstein with positive scalar curvature [4], [17], due to the Kodaira-Baily Vanishing Theorem [3], [4], H 1 (Z, K −1/n+1 ) vanishes. Therefore, the third summand in (6) vanishes.…”

Section: Lemma 6 Let Z Be the Twistor Space Of A Complete 3-sasakianmentioning

confidence: 99%

“…Boyer, Galicki and Mann find that over any quaternionic Kähler manifold, there is a principal fiber bundle with group SO (3) such that the total space is a 3-Sasakian manifold. More important, they find that every complete 3-Sasakian manifold S fibers over a quaternionic Kähler orbifold M [5].…”

Section: Introductionmentioning

confidence: 99%

A note on rigidity of 3-Sasakian manifolds

Pedersen¹,

Poon

1999

Proc. Amer. Math. Soc.

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“…Thus they deduced Theorem 1.2 from Kodaira-Baily vanishing theorem for complex orbifold due to Baily [4].…”

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confidence: 93%

Deformation of Sasakian metrics

Nozawa

2013

Trans. Amer. Math. Soc.

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Abstract. Deformations of the Reeb flow of a Sasakian manifold as transversely Kähler flows may not admit compatible Sasakian metrics. We show that the triviality of the (0, 2)-component of the basic Euler class characterizes the existence of compatible Sasakian metrics for given small deformations of the Reeb flow as transversely holomorphic Riemannian flows. We also prove a Kodaira-Akizuki-Nakano type vanishing theorem for basic Dolbeault cohomology of homologically orientable transversely Kähler foliations. As a consequence of these results, we show that any small deformations of the Reeb flow of a positive Sasakian manifold admit compatible Sasakian metrics.

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On the Imbedding of V-Manifolds in Projective Space

Cited by 86 publications

References 0 publications

Kontsevich–Witten model from 2+1 gravity: new exact combinatorial solution

Kontsevich–Witten model from 2+1 gravity: new exact combinatorial solution

A note on rigidity of 3-Sasakian manifolds

Deformation of Sasakian metrics

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