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We consider two basic problems of algebraic topology: the extension problem and the computation of higher homotopy groups, from the point of view of computability and computational complexity. The extension problem is the following: Given topological space ...
We provide a geometric characterization of rigidity of equality cases in Ehrhard ' s symmetrization inequality for Gaussian perimeter. This condition is formulated in terms of a new measure-theoretic notion of connectedness for Borel sets, inspired by Fede ...
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 ...
A compact Kahler manifold X is shown to be simply connected if its 'symmetric cotangent algebra' is trivial. Conjecturally, such a manifold should even be rationally connected. The relative version is also shown: a proper surjective connected holomorphic m ...
A method for achieving a representation of an object within a data structure for a Computer Aided Design system employing a Medial Axis Transformation (MAT), the representation of the object comprising a set of adjacent bounded surface elements called MAT ...
Let K be a comonad on a model category M. We provide conditions under which the associated category of K-coalgebras admits a model category structure such that the forgetful functor to M creates both cofibrations and weak equivalences. We provide concrete ...
For several computational problems in homotopy theory, we obtain algorithms with running time polynomial in the input size. In particular, for every fixed k >= 2, there is a polynomial-time algorithm that, for a 1-connected topological space X given as a f ...
We present an efficient matching method for generalized geometric graphs. Such graphs consist of vertices in space connected by curves and can represent many real world structures such as road networks in remote sensing, or vessel networks in medical imagi ...
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 consider a natural subclass of harmonic maps from a surface into G/T, namely cyclic primitive maps. Here G is any simple real Lie group (not necessarily compact), T is a Cartan subgroup and both are chosen so that there is a Coxeter automorphism on G(C) ...
