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Gravity and the Noncommutative Residue for Manifolds with Boundary ∗
, 2006
"... Abstract We prove a KastlerKalauWalze type theorem for the Dirac operator and the signature operator for 3,4dimensional manifolds with boundary. As a corollary, we give two kinds of operator theoretic explanations of the gravitational action in the case of 4dimensional manifolds with flat bounda ..."
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Abstract We prove a KastlerKalauWalze type theorem for the Dirac operator and the signature operator for 3,4dimensional manifolds with boundary. As a corollary, we give two kinds of operator theoretic explanations of the gravitational action in the case of 4dimensional manifolds with flat boundary. Subj. Class.: Noncommutative global analysis; Noncommutative differential geometry. MSC: 58G20; 53A30; 46L87
Differential forms and the noncommutative residue for manifolds with boundary in the nonproduct
, 2006
"... Abstract In this paper, for an even dimensional compact manifold with boundary which has the nonproduct metric near the boundary, we use the noncommutative residue to define a conformal invariant pair. For a 4dimensional manifold, we compute this conformal invariant pair under some conditions and ..."
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Cited by 8 (3 self)
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Abstract In this paper, for an even dimensional compact manifold with boundary which has the nonproduct metric near the boundary, we use the noncommutative residue to define a conformal invariant pair. For a 4dimensional manifold, we compute this conformal invariant pair under some conditions and point out the way of computations in the general.
A NOTE ON THE EINSTEINHILBERT ACTION AND DIRAC OPERATORS ON Rn
"... Abstract. We prove an extension to Rn, endowed with a suitable metric, of the relation between the EinsteinHilbert action and the Dirac operator which holds on closed spin manifolds. By means of complex powers, we first define the regularised Wodzicki Residue for a class of operators globally defin ..."
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Abstract. We prove an extension to Rn, endowed with a suitable metric, of the relation between the EinsteinHilbert action and the Dirac operator which holds on closed spin manifolds. By means of complex powers, we first define the regularised Wodzicki Residue for a class of operators globally defined onRn. The result is then obtained by using the properties of heat kernels and generalised Laplacians.
The KastlerKalauWalze type theorem for 6dimensional manifolds with boundary, arXiv: math.DG/1211.6223
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Some Conformal Invariants from the Noncommutative Residue for Manifolds with Boundary ⋆
"... Abstract. We review previous work of Alain Connes, and its extension by the author, on some conformal invariants obtained from the noncommutative residue on even dimensional compact manifolds without boundary. Inspired by recent work of Yong Wang, we also address possible generalizations of these co ..."
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Abstract. We review previous work of Alain Connes, and its extension by the author, on some conformal invariants obtained from the noncommutative residue on even dimensional compact manifolds without boundary. Inspired by recent work of Yong Wang, we also address possible generalizations of these conformal invariants to the setting of compact manifolds with boundary. Key words: manifolds with boundary; noncommutative residue; Fredholm module; conformal invariants 2000 Mathematics Subject Classification: 53A30 1
Yang.: Dirac operators with torsion and the noncommutative residue for manifolds with boundary
 J. Geom. Phys
, 2014
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KastlerKalauWalze type theorem for Manifolds with Boundary
, 907
"... dimensional volumes and the ..."
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3 Noncommutative Residue and Dirac operators for Manifolds with the Conformal RobertsonWalker metric
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