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In 1912 Bieberbach proved that every compact flat Riemannian manifold M is
finitely covered by a flat torus. More precisely, M has the form (F\G)/H where
G is a group of translations of Euclidean ...
A further generalization of the colourful Caratheodory theorem
Colourful Caratheodory theorem colourful simplicial depth discrete geometry
2011/10/8
Abstract: Given d+1 sets, or colours, S_1, S_2,...,S_{d+1} of points in R^d, a colourful set is a set S in the union of the S_i such that the intersection of S with any S_i is of cardinality at most 1...
A generalization of The Dress construction for a Tambara functor, and polynomial Tambara functors
A generalization Dress construction Tambara functor polynomial Tambara functors
2011/1/19
For a finite group G, (semi-)Mackey functors and (semi-)Tambara functors are regarded as G-bivariant analogs of (semi-)groups and (semi-)rings respectively. In fact if G is trivial, they agree with th...
Generalization of the Bollobás-Riordan polynomial for tensor graphs
(multivariate) topological graph polynomials group eld theory
2011/1/19
Tensor models are used nowadays for implementing a fundamental theory of quan-tum gravity. We de ne here a polynomial T encoding the supplementary topological information.