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There is a classical "duality" between homotopy and homology groups in that homotopy groups are compatible with homotopy pullbacks (every homotopy pullback gives rise to a long exact sequence in homotopy), while homology groups are compatible with homotopy ...
We present an affine-invariant non-stationary subdivision scheme for the recursive refinement of any triangular mesh that is regular or has extraordinary vertices of valence 4. In particular, when applied to an arbitrary convex octahedron, it produces a $ ...
Let X be a simplicial set. We construct a novel adjunction be- tween the categories RX of retractive spaces over X and ComodX+ of X+- comodules, then apply recent work on left-induced model category structures [5], [16] to establish the existence of a left ...
Localization microscopy such as STORM/PALM can achieve a nanometer scale spatial resolution by iteratively localizing fluorescence molecules. It was shown that imaging of densely activated molecules can accelerate temporal resolution which was considered a ...
We formulate the Nahm transform in the context of parabolic Higgs bundles on P^1 and extend its scope in completely algebraic terms. This transform requires parabolic Higgs bundles to satisfy an admissibility condition and allows Higgs fields to have poles ...
The Galilei group involves mass as a central charge. We show that the associated superselection rule is incompatible with the observed phenomenology of superfluid helium 4: this is recovered only under the assumption that mass is spontaneou.519 broken. Thi ...
My dissertation, ‘Periodicity and Rural Urban Dynamics’, hypothesizes that the simultaneous experience of strongly contrasting sensations is pleasurable, and that ‘abrupt urbanism’ can enhance both rural and urban experience. This article investigates the ...
Spatial compactification on R(3)xS(L)(1), at small S-1-size L often leads to a calculable vacuum structure, where various "topological molecules" are responsible for confinement and the realization of the center and discrete chiral symmetries. Within this ...
In this paper we investigate the physical spectrum of the gravitational theory based on the Poincare group with terms that are at most quadratic in tetrad and spin connection, allowing for the presence of parity-even as well as parity-odd invariants. We de ...
Let be a symmetric space of noncompact type. A result of Gelander provides exponential upper bounds in terms of the volume for the torsion homology of the noncompact arithmetic locally symmetric spaces . We show that under suitable assumptions on this resu ...
