15,814 research outputs found
Exponential separation in 4-manifolds
We use a new geometric construction, grope splitting, to give a sharp bound
for separation of surfaces in 4-manifolds. We also describe applications of
this technique in link-homotopy theory, and to the problem of locating
pi_1-null surfaces in 4-manifolds. In our applications to link-homotopy, grope
splitting serves as a geometric substitute for the Milnor group.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol4/paper13.abs.htm
Subexponential groups in 4-manifold topology
We present a new, more elementary proof of the Freedman-Teichner result that
the geometric classification techniques (surgery, s-cobordism, and
pseudoisotopy) hold for topological 4-manifolds with groups of subexponential
growth. In an appendix Freedman and Teichner give a correction to their
original proof, and reformulate the growth estimates in terms of coarse
geometry.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol4/paper14.abs.htm
The Holography of F-maximization
We find new supersymmetric backgrounds of gauged supergravity
in four Euclidean dimensions that are dual to deformations of ABJM theory on
. The deformations encode the most general choice of symmetry
used to define the theory on . We work within an truncation
of the supergravity theory obtained via a group theory argument.
We find perfect agreement between the free energy computed from our
supergravity backgrounds and the previous field theory computations of the same
quantity based on supersymmetric localization and matrix model techniques.Comment: 48 pages; v2 minor improvement
Alexander duality, gropes and link homotopy
We prove a geometric refinement of Alexander duality for certain 2-complexes,
the so-called gropes, embedded into 4-space. This refinement can be roughly
formulated as saying that 4-dimensional Alexander duality preserves the
disjoint Dwyer filtration. In addition, we give new proofs and extended
versions of two lemmas of Freedman and Lin which are of central importance in
the A-B-slice problem, the main open problem in the classification theory of
topological 4-manifolds. Our methods are group theoretical, rather than using
Massey products and Milnor \mu-invariants as in the original proofs.Comment: 19 pages. Published copy, also available at
http://www.maths.warwick.ac.uk/gt/GTVol1/paper5.abs.htm
Continuous distributions of D3-branes and gauged supergravity
States on the Coulomb branch of N=4 super-Yang-Mills theory are studied from
the point of view of gauged supergravity in five dimensions. These
supersymmetric solutions provide examples of consistent truncation from type
IIB supergravity in ten dimensions. A mass gap for states created by local
operators and perfect screening for external quarks arise in the supergravity
approximation. We offer an interpretation of these surprising features in terms
of ensembles of brane distributions.Comment: 19 pages, two figures, latex. v2: reference added, small corrections.
v3: corrected unbounded spectrum erro
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