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622
Absolutely graded Floer homologies and intersection forms for fourmanifolds with boundary
 Advances in Mathematics 173
, 2003
"... Abstract. In [22], we introduced absolute gradings on the threemanifold invariants developed in [21] and [20]. Coupled with the surgery long exact sequences, we obtain a number of three and fourdimensional applications of this absolute grading including strengthenings of the “complexity bounds ” ..."
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Cited by 183 (27 self)
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Abstract. In [22], we introduced absolute gradings on the threemanifold invariants developed in [21] and [20]. Coupled with the surgery long exact sequences, we obtain a number of three and fourdimensional applications of this absolute grading including strengthenings of the “complexity bounds ” derived in [20], restrictions on knots whose surgeries give rise to lens spaces, and calculations of HF + for a variety of threemanifolds. Moreover, we show how the structure of HF + constrains the exoticness of definite intersection forms for smooth fourmanifolds which bound a given threemanifold. In addition to these new applications, the techniques also provide alternate proofs of Donaldson’s diagonalizability theorem and the Thom conjecture for CP 2. 1.
Chern–Simons Perturbation Theory
 II,” J. Diff. Geom
, 1994
"... Abstract. We study the perturbation theory for three dimensional Chern–Simons quantum field theory on a general compact three manifold without boundary. We show that after a simple change of variables, the action obtained by BRS gauge fixing in the Lorentz gauge has a superspace formulation. The bas ..."
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Cited by 170 (2 self)
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Abstract. We study the perturbation theory for three dimensional Chern–Simons quantum field theory on a general compact three manifold without boundary. We show that after a simple change of variables, the action obtained by BRS gauge fixing in the Lorentz gauge has a superspace formulation. The basic properties of the propagator and the Feynman rules are written in a precise manner in the language of differential forms. Using the explicit description of the propagator singularities, we prove that the theory is finite. Finally the anomalous metric dependence of the 2loop partition function on the Riemannian metric (which was introduced to define the gauge fixing) can be cancelled by a local counterterm as in the 1loop case [28]. In fact, the counterterm is equal to the Chern–Simons action of the metric connection, normalized precisely as one would expect based on the framing dependence of Witten’s exact solution.
Anomalies in string theory with Dbranes
, 1999
"... This paper is devoted to studying global anomalies in the worldsheet path integral of Type II superstring theory in the presence of Dbranes. We will not consider orientifolds (or Type I superstrings) and so our string worldsheets will be oriented Riemann surfaces, mapped to a spacetime manifold Y, ..."
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Cited by 162 (9 self)
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This paper is devoted to studying global anomalies in the worldsheet path integral of Type II superstring theory in the presence of Dbranes. We will not consider orientifolds (or Type I superstrings) and so our string worldsheets will be oriented Riemann surfaces, mapped to a spacetime manifold Y, which is endowed with a spin structure since the model contains fermions. The first
Homology of pseudodifferential operators on manifolds with corners I. Manifolds with boundary
, 1996
"... Respectfully dedicate to Professor M. Sato on the occasion of his 70th birthday Abstract. Let X be a compact manifold with boundary. Suppose that the boundary is fibred, φ: ∂X − → Y, and let x ∈ C ∞ (X) be a boundary defining function. This data fixes the space of ‘fibred cusp ’ vector fields, consi ..."
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Cited by 138 (26 self)
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Respectfully dedicate to Professor M. Sato on the occasion of his 70th birthday Abstract. Let X be a compact manifold with boundary. Suppose that the boundary is fibred, φ: ∂X − → Y, and let x ∈ C ∞ (X) be a boundary defining function. This data fixes the space of ‘fibred cusp ’ vector fields, consisting of those vector fields V on X satisfying V x = O(x 2) and which are tangent to the fibres of φ; it is a Lie algebra and C ∞ (X) module. This Lie algebra is quantized to the ‘small calculus ’ of pseudodifferential operators Ψ ∗ Φ (X). Mapping properties including boundedness, regularity, Fredholm condition and symbolic maps are discussed for this calculus. The spectrum of the Laplacian of an ‘exact fibred cusp ’ metric is analyzed as is the wavefront set associated to the calculus.
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 110 (9 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.
Quadratic functions in geometry, topology,and mtheory
"... 2. Determinants, differential cocycles and statement of results 5 ..."
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Cited by 109 (4 self)
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2. Determinants, differential cocycles and statement of results 5
Selfdual instantons and holomorphic curves
 Annals of Mathematics 139
, 1994
"... 2. Floer homology for symplectic fixed points ..."
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Embedded surfaces and the structure of Donaldson’s polynomial invariants
 J. Differential Geom
, 1995
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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 79 (13 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.