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Around Podewski's conjecture

Krzysztof Krupiński, Predrag Tanović, Frank O. Wagner (2013)

Fundamenta Mathematicae

A long-standing conjecture of Podewski states that every minimal field is algebraically closed. Known in positive characteristic, it remains wide open in characteristic zero. We reduce Podewski's conjecture to the (partially) ordered case, and we conjecture that such fields do not exist. We prove the conjecture in case the incomparability relation is transitive (the almost linear case). We also study minimal groups with a (partial) order, and give a complete classification of...

Around the Borromean link.

José María Montesinos Amilibia (2008)

RACSAM

This is a survey of some consequences of the fact that the fundamental group of the orbifold with singular set the Borromean link and isotropy cyclic of order 4 is a universal kleinian group.

Asphericity of symmetric presentations

Fulvia Spaggiari (2006)

Publicacions Matemàtiques

Using the notion of relative presentation due to Bogley and Pride, we give a new proof of a theorem of Prishchepov on the asphericity of certain symmetric presentations of groups. Then we obtain further results and applications to topology of low-dimensional manifolds.

Asymptotic Behaviour of Colength of Varieties of Lie Algebras

Mishchenko, S., Zaicev, M. (2000)

Serdica Mathematical Journal

This project was partially supported by RFBR, grants 99-01-00233, 98-01-01020 and 00-15-96128.We study the asymptotic behaviour of numerical characteristics of polynomial identities of Lie algebras over a field of characteristic 0. In particular we investigate the colength for the cocharacters of polynilpotent varieties of Lie algebras. We prove that there exist polynilpotent Lie varieties with exponential and overexponential colength growth. We give the exact asymptotics for the colength of a product...

Asymptotic dimension of discrete groups

A. Dranishnikov, J. 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.

Asymptotic dimension of one relator groups

Dmitry Matsnev (2008)

Colloquium Mathematicae

We show that one relator groups viewed as metric spaces with respect to the word-length metric have finite asymptotic dimension in the sense of Gromov, and we give an improved estimate of that dimension in terms of the relator length. The construction is similar to one of Bell and Dranishnikov, but we produce a sharper estimate.

Asymptotic laws for geodesic homology on hyperbolic manifolds with cusps

Martine Babillot, Marc Peigné (2006)

Bulletin de la Société Mathématique de France

We consider a large class of non compact hyperbolic manifolds M = ℍ n / Γ with cusps and we prove that the winding process ( Y t ) generated by a closed 1 -form supported on a neighborhood of a cusp 𝒞 , satisfies a limit theorem, with an asymptotic stable law and a renormalising factor depending only on the rank of the cusp 𝒞 and the Poincaré exponent δ of Γ . No assumption on the value of δ is required and this theorem generalises previous results due to Y. Guivarc’h, Y. Le Jan, J. Franchi and N. Enriquez.

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