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92
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 55 (5 self)
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1 Transverse measure for flows 4 2 Transverse measure for foliations 6
Scalar curvature and geometrization conjectures for 3manifolds
 in Comparison Geometry (Berkeley 1993–94), MSRI Publications
, 1997
"... Abstract. We first summarize very briefly the topology of 3manifolds and the approach of Thurston towards their geometrization. After discussing some general properties of curvature functionals on the space of metrics, we formulate and discuss three conjectures that imply Thurston’s Geometrization ..."
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Cited by 30 (8 self)
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Abstract. We first summarize very briefly the topology of 3manifolds and the approach of Thurston towards their geometrization. After discussing some general properties of curvature functionals on the space of metrics, we formulate and discuss three conjectures that imply Thurston’s Geometrization Conjecture for closed oriented 3manifolds. The final two sections present evidence for the validity of these conjectures and outline an approach toward their proof.
Spectral Asymmetry, Zeta Functions and the Noncommutative Residue
"... Abstract. In this paper, motivated by an approach developed by Wodzicki, we look at the spectral asymmetry of elliptic ΨDO’s in terms of theirs zeta functions. First, using asymmetry formulas of Wodzicki we study the spectral asymmetry of odd elliptic ΨDO’s and of geometric Dirac operators. In parti ..."
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Cited by 18 (7 self)
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Abstract. In this paper, motivated by an approach developed by Wodzicki, we look at the spectral asymmetry of elliptic ΨDO’s in terms of theirs zeta functions. First, using asymmetry formulas of Wodzicki we study the spectral asymmetry of odd elliptic ΨDO’s and of geometric Dirac operators. In particular, we show that the eta function of a selfadjoint elliptic odd ΨDO is regular at every integer point when the dimension and the order have opposite parities (this generalizes a well known result of BransonGilkey for Dirac operators), and we relate the spectral asymmetry of a Dirac operator on a Clifford bundle to the Riemmanian geometric data, which yields a new spectral interpretation of the Einstein action from gravity. We also obtain a large class of examples of elliptic ΨDO’s for which the regular values at the origin of the (local) zeta functions can easily be seen to be independent of the spectral cut. On the other hand, we simplify the proofs of two wellknown and difficult results of Wodzicki: (i) The independence with respect to the spectral cut of the regular value at the origin of the zeta function of an elliptic ΨDO; (ii) The vanishing of the noncommutative residue of a zero’th order ΨDO projector. These results were proved by Wodzicki using a quite difficult and involved characterization of local invariants of spectral asymmetry, which we can bypass here. Finally, in an appendix we give a new proof of the aforementioned asymmetry formulas of Wodzicki. 1.
On boundary value problems for Dirac type operators. I. Regularity and self–adjointness
, 1999
"... ..."
Conformal Geometry And Global Invariants
 Diff. Geom. Appl
, 1991
"... . Continuing our study of global conformal invariants for Riemannian manifolds, we find new classes of such invariants corresponding to boundary value problems and to Lefschetz fixed point theorems. We also study the eta invariant, functional determinants, and analytic continuation to metrics of ind ..."
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Cited by 12 (5 self)
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. Continuing our study of global conformal invariants for Riemannian manifolds, we find new classes of such invariants corresponding to boundary value problems and to Lefschetz fixed point theorems. We also study the eta invariant, functional determinants, and analytic continuation to metrics of indefinite signature. In particular, we find global invariants of CR manifolds coming from bundles which support Lorentz metrics. 0. Introduction Given a geometric structure on a manifold M , one may attempt to study the topology and geometry of M via the global behavior of solutions to naturally associated partial differential equations. Often the functional analytic constructs in this situation will reveal deep facts about M , locally as well as globally. A standard example is that of the Laplace operator \Delta on differential forms in a compact, Riemannian, mdimensional, smooth manifold (M; g) without boundary: here asymptotically, (0.1) Tr L 2 exp(\Gammat\Delta) ¸ t \Gammam=2 1 X i=...
Twisted index theory on good orbifolds, I: noncommutative Bloch theory
 Commun. Contemp. Math. Vol1
, 1999
"... Abstract. We study the twisted index theory of elliptic operators on orbifold covering spaces of compact good orbifolds, which are invariant under a projective action of the orbifold fundamental group. We apply these results to obtain qualitative results on real and complex hyperbolic spaces in 2 an ..."
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Cited by 11 (7 self)
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Abstract. We study the twisted index theory of elliptic operators on orbifold covering spaces of compact good orbifolds, which are invariant under a projective action of the orbifold fundamental group. We apply these results to obtain qualitative results on real and complex hyperbolic spaces in 2 and 4 dimensions, related to generalizations of the BetheSommerfeld conjecture and the Ten Martini Problem, on the spectrum of self adjoint elliptic operators which are invariant under a projective action of a discrete cocompact group.