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36
Configuration spaces and Vassiliev classes in any dimension
"... Abstract. The real cohomology of the space of imbeddings of S 1 into R n, n> 3, is studied both by using configuration space integrals and by considering the restriction of classes defined on the corresponding spaces of immersions. Nontrivial classes are explicitly constructed. The cohomology classe ..."
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Cited by 41 (5 self)
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Abstract. The real cohomology of the space of imbeddings of S 1 into R n, n> 3, is studied both by using configuration space integrals and by considering the restriction of classes defined on the corresponding spaces of immersions. Nontrivial classes are explicitly constructed. The cohomology classes obtained by configuration space integrals generalize in a nontrivial way the Vassiliev knot invariants obtained in three dimensions from the Chern–Simons perturbation theory. 1.
Higherdimensional BF theories in the BatalinVilkovisky formalism: The BV action and generalized Wilson loops
 math.QA/0010172 THE AKSZ FORMULATION OF THE POISSON SIGMA MODEL 19
"... ABSTRACT. This paper analyzes in details the Batalin–Vilkovisky quantization procedure for BF theories on ndimensional manifolds and describes a suitable superformalism to deal with the master equation and the search of observables. In particular, generalized Wilson loops for BF theories with addit ..."
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Cited by 17 (9 self)
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ABSTRACT. This paper analyzes in details the Batalin–Vilkovisky quantization procedure for BF theories on ndimensional manifolds and describes a suitable superformalism to deal with the master equation and the search of observables. In particular, generalized Wilson loops for BF theories with additional polynomial Binteractions are discussed in any dimensions. The paper also contains the explicit proofs to the Theorems stated in [16].
Anomaly cancellation in Mtheory: a critical review, Nucl.Phys
 B
"... We carefully review the basic examples of anomaly cancellation in Mtheory: the 5brane anomalies and the anomalies on S 1 /Z2. This involves cancellation between quantum anomalies and classical inflow from topological terms. To correctly fix all coefficients and signs, proper attention is paid to i ..."
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Cited by 10 (3 self)
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We carefully review the basic examples of anomaly cancellation in Mtheory: the 5brane anomalies and the anomalies on S 1 /Z2. This involves cancellation between quantum anomalies and classical inflow from topological terms. To correctly fix all coefficients and signs, proper attention is paid to issues of orientation, chirality and the Euclidean continuation. Independent of the conventions chosen, the ChernSimons and GreenSchwarz terms must always have the same sign. The reanalysis of the reduction to the heterotic string on S 1 /Z2 yields a surprise: a previously neglected factor forces us to slightly modify the ChernSimons term, similar to what is needed for cancelling the normal bundle anomaly of the 5brane. This modification leads to a local cancellation of the anomaly, while maintaining the Various examples of anomaly cancellation in Mtheory are based on an interplay between quantum anomalies on evendimensional submanifolds and anomaly inflow from the 11dimensional bulk through a noninvariance of a topological integral like SCS ∼ ∫ C ∧ dC ∧ dC or SGS ∼
Effective BatalinVilkovisky Theories, Equivariant Configuration Spaces and Cyclic Chains
, 2008
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The Universal Perturbative Quantum 3manifold Invariant, RozanskyWitten Invariants, and the Generalized Casson Invariant
, 1999
"... Let Z LMO be the 3manifold invariant of [LMO]. It is shown that Z LMO (M ) = 1, if the first Betti number of M , b 1 (M ), is greater than 3. If b 1 (M ) = 3, then Z LMO (M ) is completely determined by the cohomology ring of M . A relation of Z LMO with the RozanskyWitten invariants Z ..."
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Cited by 8 (1 self)
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Let Z LMO be the 3manifold invariant of [LMO]. It is shown that Z LMO (M ) = 1, if the first Betti number of M , b 1 (M ), is greater than 3. If b 1 (M ) = 3, then Z LMO (M ) is completely determined by the cohomology ring of M . A relation of Z LMO with the RozanskyWitten invariants Z RW X [M ] is established at a physical level of rigour. We show that Z RW X [M ] satisfies appropriate connected sum properties suggesting that the generalized Casson invariant ought to be computable from the LMO invariant.
Feynman Diagrams for Pedestrians and Mathematicians
"... 1.1. About these lecture notes. For centuries physics was a potent source providing mathematics with interesting ideas and problems. In the last decades something new started to happen: physicists started to provide mathematicians also with technical tools, methods, and solutions. This process seem ..."
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Cited by 8 (0 self)
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1.1. About these lecture notes. For centuries physics was a potent source providing mathematics with interesting ideas and problems. In the last decades something new started to happen: physicists started to provide mathematicians also with technical tools, methods, and solutions. This process seem to be especially
A toy model of the M5brane: Anomalies of monopole strings in five dimensions,” Annals Phys
, 2002
"... We study a fivedimensional field theory which contains a monopole (string) solution with chiral fermion zero modes. This monostring solution is a close analog of the fivebrane solution of Mtheory. The cancellation of normal bundle anomalies parallels that for the Mtheory fivebrane, in particular, ..."
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Cited by 6 (2 self)
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We study a fivedimensional field theory which contains a monopole (string) solution with chiral fermion zero modes. This monostring solution is a close analog of the fivebrane solution of Mtheory. The cancellation of normal bundle anomalies parallels that for the Mtheory fivebrane, in particular, the presence of a ChernSimons term in the lowenergy effective U(1) gauge theory plays a central role. We comment on the relationship between the the microscopic analysis of the worldvolume theory and the lowenergy analysis and draw some cautionary lessons for Mtheory.
Configuration space integrals and invariants for 3manifolds and knots, from “Lowdimensional topology
, 1998
"... In this paper we give a brief description of the way proposed in [4] of associating invariants of both 3dimensional rational homology spheres (r.h.s.) and knots in r.h.s.’s to certain combinations of trivalent diagrams. In addition, we discuss the relation between this construction ..."
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Cited by 6 (3 self)
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In this paper we give a brief description of the way proposed in [4] of associating invariants of both 3dimensional rational homology spheres (r.h.s.) and knots in r.h.s.’s to certain combinations of trivalent diagrams. In addition, we discuss the relation between this construction
A superanalogue of Kontsevich’s theorem on graph homology
 Lett. Math. Phys
, 2006
"... Abstract. In this paper we will prove a superanalogue of a wellknown result by Kontsevich which states that the homology of a certain complex which is generated by isomorphism classes of oriented graphs can be calculated as the Lie algebra homology of an infinitedimensional Lie algebra of symplec ..."
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Cited by 5 (4 self)
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Abstract. In this paper we will prove a superanalogue of a wellknown result by Kontsevich which states that the homology of a certain complex which is generated by isomorphism classes of oriented graphs can be calculated as the Lie algebra homology of an infinitedimensional Lie algebra of symplectic vector fields. 1.
Master equation and perturbative Chern–Simons theory,” preprint
"... Abstract. We extend the ChernSimons perturbative invariant of Axelrod and Singer [1] to not acyclic connections. We construct a solution of the quantum master equation on the space of functions on the cohomology of the connection. We prove that this solution is well defined up to master homotopy. W ..."
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Cited by 4 (1 self)
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Abstract. We extend the ChernSimons perturbative invariant of Axelrod and Singer [1] to not acyclic connections. We construct a solution of the quantum master equation on the space of functions on the cohomology of the connection. We prove that this solution is well defined up to master homotopy. We study the analogous problem for knot invariants. 1. introduction Let M be a compact oriented three manifold. Consider a flat connection on a principal bundle over M with compact structural group. Let g be the related Lie algebra bundle. If the cohomology H ∗ (M, g) of the flat connection is trivial, Axelrod and Singer ([1]) and Kontsevich ([5]) proved that the perturbative expansion of the ChernSimons theory leads to topological invariants of the manifold M. Non acyclic connections have been recently considered by Costello ([2]). The perturbative expansion of the partition function should lead to a function on the cohomology of the connection H ∗ (M, g) that solves the quantum master equation