14,756 research outputs found
Zoll Metrics, Branched Covers, and Holomorphic Disks
We strengthen our previous results regarding the moduli spaces of Zoll
metrics and Zoll projective structures on S^2. In particular, we describe a
concrete, open condition which suffices to guarantee that a totally real
embedding of RP^2 in CP_2 arises from a unique Zoll projective structure on the
2-sphere. Our methods ultimately reflect the special role such structures play
in the initial value problem for the 3-dimensional Lorentzian Einstein-Weyl
equations.Comment: 21 pages, LaTeX2
Zoll Manifolds and Complex Surfaces
We classify compact surfaces with torsion-free affine connections for which
every geodesic is a simple closed curve. In the process, we obtain completely
new proofs of all the major results concerning the Riemannian case.
In contrast to previous work, our approach is twistor-theoretic, and depends
fundamentally on the fact that, up to biholomorphism, there is only one complex
structure on CP2
Nonlinear Gravitons, Null Geodesics, and Holomorphic Disks
We develop a global twistor correspondence for pseudo-Riemannian conformal
structures of signature (++--) with self-dual Weyl curvature. Near the
conformal class of the standard indefinite product metric on S^2 x S^2, there
is an infinite-dimensional moduli space of such conformal structures, and each
of these has the surprising global property that its null geodesics are all
periodic. Each such conformal structure arises from a family of holomorphic
disks in CP_3 with boundary on some totally real embedding of RP^3 into CP_3.
An interesting sub-class of these conformal structures are represented by
scalar-flat indefinite K\"ahler metrics, and our methods give particularly
sharp results in this more restrictive setting.Comment: 56 pages, LaTeX2
The Einstein-Weyl Equations, Scattering Maps, and Holomorphic Disks
We show that conformally compact, globally hyperbolic, Lorentzian
Einstein-Weyl 3-manifolds are in natural one-to-one correspondence with
orientation-reversing diffeomorphisms of the 2-sphere. The proof hinges on a
holomorphic-disk analog of Hitchin's mini-twistor correspondence.Comment: 11 pages, LaTeX2e. Revised version strengthens result and completes
proo
Geometric realization and K-theoretic decomposition of C*-algebras
Suppose that A is a separable C*-algebra and that G_* is a (graded) subgroup
of K_*(A). Then there is a natural short exact sequence 0 \to G_* \to K_*(A)
\to K_*(A)/G_* \to 0.
In this note we demonstrate how to geometrically realize this sequence at the
level of C*-algebras. As a result, we KK-theoretically decompose A as 0 \to
A\otimes \Cal K \to A_f \to SA_t \to 0 where K_*(A_t) is the torsion subgroup
of K_*(A) and K_*(A_f) is its torsionfree quotient. Then we further decompose
A_t : it is KK-equivalent to \oplus_p A_p where K_*(A_p) is the p-primary
subgroup of the torsion subgroup of K_*(A). We then apply this realization to
study the Kasparov group K^*(A) and related objects.Comment: 9 pages.To appear in International J. Mat
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