arXiv subjects

Holger Kammeyer

Publications and source records attributed to Holger Kammeyer.

22 records · Page 2Linked to original sources

arXiv2017

The shrinkage type of knots

We study spectral gaps of cellular differentials for finite cyclic coverings of knot complements. Their asymptotics can be expressed in terms of irrationality exponents associated with ratios of logarithms of algebraic numbers determined by the first two Alexander polynomials. From this point of view it is natural to subdivide all knots into three different types. We show that examples of all types abound and discuss what happens for twist and torus knots as well as knots with few crossings.

math.GT↗

arXiv2015

The Farrell-Jones conjecture for arbitrary lattices in virtually connected Lie groups

We prove the K- and the $L$-theoretic Farrell-Jones conjecture with coefficients in additive categories and with finite wreath products for arbitrary lattices in virtually connected Lie groups.

math.KT↗

arXiv2013

An explicit rational structure for real semisimple Lie algebras

We construct a convenient basis for all real semisimple Lie algebras by means of an adapted Chevalley basis of the complexification. It determines rational and in fact half-integer structure constants which we express only in terms of the root system and the involution that defines the real structure.

math.RT↗

arXiv2013

L2-invariants of nonuniform lattices in semisimple Lie groups

We compute L2-invariants of certain nonuniform lattices in semisimple Lie groups by means of the Borel-Serre compactification of arithmetically defined locally symmetric spaces. The main results give new estimates for Novikov-Shubin numbers and vanishing L2-torsion for lattices in groups with even deficiency. We discuss applications to Gromov's Zero-in-the-Spectrum Conjecture as well as to a proportionality conjecture for the L2-torsion of measure equivalent groups.

math.AT↗