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421
Equivariant Cohomology, Koszul Duality, and the Localization Theorem
 Invent. Math
, 1998
"... This paper concerns three aspects of the action of a compact group K on a space ..."
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Cited by 148 (4 self)
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This paper concerns three aspects of the action of a compact group K on a space
Lectures on 2D YangMills Theory, Equivariant Cohomology and Topological Field Theories
, 1996
"... These are expository lectures reviewing (1) recent developments in twodimensional YangMills theory and (2) the construction of topological field theory Lagrangians. Topological field theory is discussed from the point of view of infinitedimensional differential geometry. We emphasize the unifying ..."
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Cited by 99 (7 self)
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These are expository lectures reviewing (1) recent developments in twodimensional YangMills theory and (2) the construction of topological field theory Lagrangians. Topological field theory is discussed from the point of view of infinitedimensional differential geometry. We emphasize the unifying role of equivariant cohomology both as the underlying principle in the formulation of BRST transformation laws and as a central concept in the geometrical interpretation of topological field theory path integrals.
E(8) Gauge Theory and a Derivation of Ktheory from Mtheory
"... The partition function of RamondRamond pform fields in Type IIA supergravity on a tenmanifold X contains subtle phase factors that are associated with Tduality, selfduality, and the relation of the RR fields to Ktheory. The analogous partition function of Mtheory on X × S 1 contains subtle pha ..."
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Cited by 98 (8 self)
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The partition function of RamondRamond pform fields in Type IIA supergravity on a tenmanifold X contains subtle phase factors that are associated with Tduality, selfduality, and the relation of the RR fields to Ktheory. The analogous partition function of Mtheory on X × S 1 contains subtle phases that are similarly associated with E8 gauge theory. We analyze the detailed phase factors on the two sides and show that they agree, thereby testing Mtheory/Type IIA duality as well as the Ktheory formalism in an interesting way. We also show that certain Dbrane states wrapped on nontrivial homology cycles are actually unstable, that (−1) FL symmetry in Type IIA superstring theory depends in general on a cancellation between a fermion anomaly and an anomaly of RR fields, and that Type IIA superstring theory with no wrapped branes is welldefined only on a spacetime with W7 = 0. On leave from Institute for Advanced Study, Princeton, NJ 08540.
Gauge theory for embedded surfaces
 I, Topology
, 1993
"... (i) Topology of embedded surfaces. Let X be a smooth, simplyconnected 4manifold, and ξ a 2dimensional homology class in X. One of the features of topology in dimension 4 is the fact that, although one may always represent ξ as the fundamental class of some smoothly ..."
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Cited by 67 (6 self)
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(i) Topology of embedded surfaces. Let X be a smooth, simplyconnected 4manifold, and ξ a 2dimensional homology class in X. One of the features of topology in dimension 4 is the fact that, although one may always represent ξ as the fundamental class of some smoothly
SasakiEinstein manifolds and volume minimisation
, 2006
"... We study a variational problem whose critical point determines the Reeb vector field for a Sasaki–Einstein manifold. This extends our previous work on Sasakian geometry by lifting the condition that the manifolds are toric. We show that the Einstein–Hilbert action, restricted to a space of Sasakian ..."
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Cited by 57 (2 self)
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We study a variational problem whose critical point determines the Reeb vector field for a Sasaki–Einstein manifold. This extends our previous work on Sasakian geometry by lifting the condition that the manifolds are toric. We show that the Einstein–Hilbert action, restricted to a space of Sasakian metrics on a link L in a Calabi–Yau cone M, is the volume functional, which in fact is a function on the space of Reeb vector fields. We relate this function both to the Duistermaat– Heckman formula and also to a limit of a certain equivariant index on M that counts holomorphic functions. Both formulae may be evaluated by localisation. This leads to a general formula for the volume function in terms of topological fixed point data. As a result we prove that the volume of any Sasaki–Einstein manifold, relative to that of the round sphere, is always an algebraic number. In complex dimension n = 3 these results provide, via AdS/CFT, the geometric counterpart of a–maximisation in four dimensional superconformal field theories. We also show that our variational problem dynamically sets to zero the Futaki
A survey of foliations and operator algebras
 Proc. Sympos. Pure
, 1982
"... 1 Transverse measure for flows 4 2 Transverse measure for foliations 6 ..."
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Cited by 54 (5 self)
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1 Transverse measure for flows 4 2 Transverse measure for foliations 6
Families of Dirac operators, boundaries and the bcalculus
 Zbl 0955.58020 MR 1472895
, 1997
"... Aversion of the AtiyahPatodiSinger index theorem is proved for general families of Dirac operators on compact manifolds with boundary. Thevanishing of the analytic index of the boundary family, inK1 of the base, allows us to de ne, through an explicit trivialization, a smooth family of boundary co ..."
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Cited by 52 (11 self)
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Aversion of the AtiyahPatodiSinger index theorem is proved for general families of Dirac operators on compact manifolds with boundary. Thevanishing of the analytic index of the boundary family, inK1 of the base, allows us to de ne, through an explicit trivialization, a smooth family of boundary conditions of generalized AtiyahPatodiSinger type. The calculus of bpseudodi erential operators is then employed to establish the family index formula. A relative index formula, describing the e ect of changing the choice of the trivialization, is also given. In case the boundary family is invertible the form of the index theorem obtained by Bismut and Cheeger is recovered.