1,036 research outputs found
Embedded graph 3-coloring and flows
A graph drawn in a surface is a near-quadrangulation if the sum of the
lengths of the faces different from 4-faces is bounded by a fixed constant. We
leverage duality between colorings and flows to design an efficient algorithm
for 3-precoloring-extension in near-quadrangulations of orientable surfaces.
Furthermore, we use this duality to strengthen previously known sufficient
conditions for 3-colorability of triangle-free graphs drawn in orientable
surfaces.Comment: 53 pages, 15 figure
Baryonic branches and resolutions of Ricci-flat Kahler cones
We consider deformations of N=1 superconformal field theories that are
AdS/CFT dual to Type IIB string theory on Sasaki-Einstein manifolds,
characterised by non-zero vacuum expectation values for certain baryonic
operators. Such baryonic branches are constructed from (partially) resolved,
asymptotically conical Ricci-flat Kahler manifolds, together with a choice of
point where the stack of D3-branes is placed. The complete solution then
describes a renormalisation group flow between two AdS fixed points. We discuss
the use of probe Euclidean D3-branes in these backgrounds as a means to compute
expectation values of baryonic operators. The Y^{p,q} theories are used as
illustrative examples throughout the paper. In particular, we present
supergravity solutions describing flows from the Y^{p,q} theories to various
different orbifold field theories in the infra-red, and successfully match this
to an explicit field theory analysis.Comment: 51 pages, v2: reference added and minor changes; v3: minor changes,
published versio
New moduli spaces of pointed curves and pencils of flat connections
It is well known that formal solutions to the Associativity Equations are the
same as cyclic algebras over the homology operad of
the moduli spaces of --pointed stable curves of genus zero. In this paper we
establish a similar relationship between the pencils of formal flat connections
(or solutions to the Commutativity Equations) and homology of a new series
of pointed stable curves of genus zero. Whereas
parametrizes trees of 's with pairwise distinct nonsingular marked
points, parametrizes strings of 's stabilized by marked
points of two types. The union of all 's forms a semigroup rather
than operad, and the role of operadic algebras is taken over by the
representations of the appropriately twisted homology algebra of this union.Comment: 37 pages, AMSTex. Several typos corrected, a reference added,
subsection 3.2.2 revised, subsection 3.2.4 adde
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Mini-Workshop: The Willmore Functional and the Willmore Conjecture
The Willmore functional evaluated on a surface immersed into Euclidean space is given by the -norm of its mean curvature. The interest for studying this functional comes from various directions. First, it arises in applications from biology and physics, where it is used to model surface tension in the Helfrich model for bilipid layers, or in General Relativity where it appears in Hawking’s quasi-local mass. Second, the mathematical properties justify consideration of the Willmore functional in its own right. The Willmore functional is one of the most natural extrinsic curvature functionals for immersions. Its critical points solve a fourth order Euler-Lagrange equation, which has all minimal surfaces as solutions
Surfaces in the complex projective plane and their mapping class groups
An orientation preserving diffeomorphism over a surface embedded in a
4-manifold is called extendable, if this diffeomorphism is a restriction of an
orientation preserving diffeomorphism on this 4-manifold. In this paper, we
investigate conditions for extendability of diffeomorphisms over surfaces in
the complex projective plane.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-25.abs.htm
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