2,547 research outputs found
Equivariant Cohomology of Rationally Smooth Group Embeddings
We describe the equivariant cohomology ring of rationally smooth projective
embeddings of reductive groups. These embeddings are the projectivizations of
reductive monoids. Our main result describes their equivariant cohomology in
terms of roots, idempotents, and underlying monoid data. Also, we characterize
those embeddings whose equivariant cohomology ring is obtained via restriction
to the associated toric variety. Such characterization is given in terms of the
closed orbits.Comment: 25 pages. Final version. To appear in Transformation Group
Involutions on S^6 with 3-dimensional fixed point set
In this article, we classify all involutions on S^6 with 3-dimensional fixed
point set. In particular, we discuss the relation between the classification of
involutions with fixed point set a knotted 3-sphere and the classification of
free involutions on homotopy CP^3's.Comment: 23 page
Minimal genera of open 4-manifolds
We study exotic smoothings of open 4-manifolds using the minimal genus
function and its analog for end homology. While traditional techniques in open
4-manifold smoothing theory give no control of minimal genera, we make progress
by using the adjunction inequality for Stein surfaces. Smoothings can be
constructed with much more control of these genus functions than the compact
setting seems to allow. As an application, we expand the range of 4-manifolds
known to have exotic smoothings (up to diffeomorphism). For example, every
2-handlebody interior (possibly infinite or nonorientable) has an exotic
smoothing, and "most" have infinitely, or sometimes uncountably many,
distinguished by the genus function and admitting Stein structures when
orientable. Manifolds with 3-homology are also accessible. We investigate
topological submanifolds of smooth 4-manifolds. Every domain of holomorphy
(Stein open subset) in the complex plane is topologically isotopic to
uncountably many other diffeomorphism types of domains of holomorphy with the
same genus functions, or with varying but controlled genus functions.Comment: 30 pages, 1 figure. v3 is essentially the version published in
Geometry and Topology, obtained from v2 by major streamlining for
readability. Several new examples added since v2; see last paragraph of
introduction for detail
Gravity Dual of a Quantum Hall Plateau Transition
We show how to model the transition between distinct quantum Hall plateaus in
terms of D-branes in string theory. A low energy theory of 2+1 dimensional
fermions is obtained by considering the D3-D7 system, and the plateau
transition corresponds to moving the branes through one another. We study the
transition at strong coupling using gauge/gravity duality and the probe
approximation. Strong coupling leads to a novel kind of plateau transition: at
low temperatures the transition remains discontinuous due to the effects of
dynamical symmetry breaking and mass generation, and at high temperatures is
only partially smoothed out.Comment: 27 pages, 6 figures, harvmac; v2, references and minor comments
added, version to be submitted to JHEP; v3, corrections to section
Conformal nets I: coordinate-free nets
We describe a coordinate-free perspective on conformal nets, as functors from
intervals to von Neumann algebras. We discuss an operation of fusion of
intervals and observe that a conformal net takes a fused interval to the fiber
product of von Neumann algebras. Though coordinate-free nets do not a priori
have vacuum sectors, we show that there is a vacuum sector canonically
associated to any circle equipped with a conformal structure. This is the first
in a series of papers constructing a 3-category of conformal nets, defects,
sectors, and intertwiners.Comment: Updated to published versio
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