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Topological and uniform structures on universal covering spaces
Universal covering maps uniform structures Algebraic Topology
2012/6/7
We discuss various uniform structures and topologies on the universal covering space $\widetilde X$ and on the fundamental group $\pi_1(X,x_0)$. We introduce a canonical uniform structure $CU(X)$ on a...
Logarithmic structures on K-theory spectra
Symmetric spectra log structures E-infinity spaces group completion topological Andre-Quillen homology
2012/4/23
We study a modified version of Rognes' logarithmic structures on structured ring spectra. In our setup, we obtain canonical logarithmic structures on connective K-theory spectra which approximate the ...
New States of Matter Suggested by New Topological Structures
New States of Matter New Topological Structures
2011/3/2
We extend the well-known Borromean and Brunnian rings to new higher order versions. Then we suggest an extension of the connection between E mov states in cold gases and Borromean and Brunnian rings t...
Exotic smooth structures on topological fibre bundles
Exotic smooth structures topological fibre bundles
2010/11/24
We use a variation of Hatcher's construction to construct virtually all stable exotic smooth structures on compact smooth manifold bundles whose fibers have sufficiently large odd dimension (at least...
Codimension one symplectic foliations and regular Poisson structures
Codimension one symplectic foliations regular Poisson structures
2010/11/30
In this short note we give a complete characterization of a certain class of compact corank one Poisson manifolds,those equipped with a closed one-form defining the symplectic foliation
and a closed ...
Stable Vortex-Bright Soliton Structures in Two-Component Bose Einstein Condensates
Soliton Structures topological charge Two-Component Bose Einstein Condensates
2010/4/1
We report the numerical realization and demonstration of robustness of certain 2-component structures in Bose-Einstein Condensates in 2 and 3 spatial dimensions with non-trivial topological charge in ...