3,798 research outputs found
Sets of generators blocking all generators in finite classical polar spaces
We introduce generator blocking sets of finite classical polar spaces. These
sets are a generalisation of maximal partial spreads. We prove a
characterization of these minimal sets of the polar spaces Q(2n,q), Q-(2n+1,q)
and H(2n,q^2), in terms of cones with vertex a subspace contained in the polar
space and with base a generator blocking set in a polar space of rank 2.Comment: accepted for J. Comb. Theory
Partial ovoids and partial spreads in symplectic and orthogonal polar spaces
We present improved lower bounds on the sizes of small maximal partial ovoids and small maximal partial spreads in the classical symplectic and orthogonal polar spaces, and improved upper bounds on the sizes of large maximal partial ovoids and large maximal partial spreads in the classical symplectic and orthogonal polar spaces. An overview of the status regarding these results is given in tables. The similar results for the hermitian classical polar spaces are presented in [J. De Beule, A. Klein, K. Metsch, L. Storme, Partial ovoids and partial spreads in hermitian polar spaces, Des. Codes Cryptogr. (in press)]
Partial ovoids and partial spreads in finite classical polar spaces
We survey the main results on ovoids and spreads, large maximal partial ovoids and large maximal partial spreads, and on small maximal partial ovoids and small maximal partial spreads in classical finite polar spaces. We also discuss the main results on the spectrum problem on maximal partial ovoids and maximal partial spreads in classical finite polar spaces
Automorphisms of free groups with boundaries
The automorphisms of free groups with boundaries form a family of groups
A_{n,k} closely related to mapping class groups, with the standard
automorphisms of free groups as A_{n,0} and (essentially) the symmetric
automorphisms of free groups as A_{0,k}. We construct a contractible space
L_{n,k} on which A_{n,k} acts with finite stabilizers and finite quotient space
and deduce a range for the virtual cohomological dimension of A_{n,k}. We also
give a presentation of the groups and calculate their first homology group.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-25.abs.htm
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