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Asymptotic dimension of discrete groups

A. DranishnikovJ. Smith — 2006

Fundamenta Mathematicae

We extend Gromov's notion of asymptotic dimension of finitely generated groups to all discrete groups. In particular, we extend the Hurewicz type theorem proven in [B-D2] to general groups. Then we use this extension to prove a formula for the asymptotic dimension of finitely generated solvable groups in terms of their Hirsch length.

Extending regular foliations

J. W. Smith — 1969

Annales de l'institut Fourier

A p -dimensional foliation F on a differentiable manifold M is said to extend provided there exists a ( p + 1 ) -dimensional foliation F ' on M with F F ' . Our main result asserts that if M and F extends over relatively compact subsets of M .

Quantum idempotence, distributivity, and the Yang-Baxter equation

J. D. H. Smith — 2016

Commentationes Mathematicae Universitatis Carolinae

Quantum quasigroups and loops are self-dual objects that provide a general framework for the nonassociative extension of quantum group techniques. They also have one-sided analogues, which are not self-dual. In this paper, natural quantum versions of idempotence and distributivity are specified for these and related structures. Quantum distributive structures furnish solutions to the quantum Yang-Baxter equation.

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