55 research outputs found
Combinatorial Heegaard Floer homology and nice Heegaard diagrams
We consider a stabilized version of hat Heegaard Floer homology of a
3-manifold Y (i.e. the U=0 variant of Heegaard Floer homology for closed
3-manifolds). We give a combinatorial algorithm for constructing this
invariant, starting from a Heegaard decomposition for Y, and give a
combinatorial proof of its invariance properties
Combinatorial Heegaard Floer homology and sign assignments
We provide an intergral lift of the combinatorial definition of Heegaard
Floer homology for nice diagrams, and show that the proof of independence using
convenient diagrams adapts to this setting.Comment: 51 pages, 32 figure
Seifert fibered contact three-manifolds via surgery
Using contact surgery we define families of contact structures on certain
Seifert fibered three-manifolds. We prove that all these contact structures are
tight using contact Ozsath-Szabo invariants. We use these examples to show
that, given a natural number n, there exists a Seifert fibered three-manifold
carrying at least n pairwise non-isomorphic tight, not fillable contact
structures.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-12.abs.htm
Ricci flow for homogeneous compact models of the universe
Using quaternions, we give a concise derivation of the Ricci tensor for
homogeneous spaces with topology of the 3-dimensional sphere. We derive
explicit and numerical solutions for the Ricci flow PDE and discuss their
properties. In the collapse (or expansion) of these models, the interplay of
the various components of the Ricci tensor are studied. We dedicate this paper
to honor the work of Josh Goldberg.Comment: 18 pages, 2 figure
An infinite family of tight, not semi-fillable contact three-manifolds
We prove that an infinite family of virtually overtwisted tight contact
structures discovered by Honda on certain circle bundles over surfaces admit no
symplectic semi-fillings. The argument uses results of Mrowka, Ozsvath and Yu
on the translation-invariant solutions to the Seiberg-Witten equations on
cylinders and the non-triviality of the Kronheimer-Mrowka monopole invariants
of symplectic fillings.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol7/paper30.abs.htm
Localization for Involutions in Floer Cohomology
We consider Lagrangian Floer cohomology for a pair of Lagrangian submanifolds in a symplectic manifold M. Suppose that M carries a symplectic involution, which preserves both submanifolds. Under various topological hypotheses, we prove a localization theorem for Floer cohomology, which implies a Smith-type inequality for the Floer cohomology groups in M and its fixed point set. Two applications to symplectic Khovanov cohomology are included.National Science Foundation (U.S.) (grant DMS-0405516)National Science Foundation (U.S.) (grant DMS-065260)European Research Council (grant ERC-2007-StG-205349
Heegaard Floer invariants of Legendrian knots in contact three--manifolds
We define invariants of null--homologous Legendrian and transverse knots in
contact 3--manifolds. The invariants are determined by elements of the knot
Floer homology of the underlying smooth knot. We compute these invariants, and
show that they do not vanish for certain non--loose knots in overtwisted
3--spheres. Moreover, we apply the invariants to find transversely non--simple
knot types in many overtwisted contact 3--manifolds.Comment: 70 pages, 30 figure
Shear-free rotating inflation
We demonstrate the existence of shear-free cosmological models with rotation
and expansion which support the inflationary scenarios. The corresponding
metrics belong to the family of spatially homogeneous models with the geometry
of the closed universe (Bianchi type IX). We show that the global vorticity
does not prevent the inflation and even can accelerate it.Comment: Revtex, 12 pages; to appear in Phys. Rev.
On closed rotating worlds
A new solution for the stationary closed world with rigid rotation is
obtained for the spinning fluid source. It is found that the spin and vorticity
are locally balanced. This model qualitatively shows that the local rotation of
the cosmological matter can be indeed related to the global cosmic vorticity,
provided the total angular momentum of the closed world is vanishing.Comment: 10 pages, Revtex, to appear in Phys. Rev. D6
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