SCIENTIFIC PROGRAMS AND ACTIVTIES

August 27, 2014

August 16-19, 2006
Workshop on Geometric Methods in Group Theory
held at Carleton University

Schedule

All the meetings will be held in the room HP 4351 (Macphail Room), in Herzberg Laboratories. The room is next to the Main Office of the School of Mathematic and Statistics. The phone number of the Main Office is 613-520-2155.

On WEDNESDAY, Aug 16 the registration begins at 9:00, in the Main Office of the School of Math and Stats (HP 4302), Herzberg Labs.

Wednesday Aug 16

10-11

Zlil Sela, Hebrew University
Diophantine geometry over groups and the elementary theory of a free group

11:15 – 12:15

Jon McCammond, UC Santa Barbara
The geometry of groups defined geometrically
Topics include Coxeter groups and buildings, Artin groups and Garside structures, Lie groups and continuous braids.

14:30-15:30 Daniel Wise, McGill University
Nonpositively Curved Cube Complexes in Geometric Group Theory

Nonpositively curved cube complexes have come to occupy an increasingly important role in geometric group theory. Surprisingly many of the groups traditionally studied by combinatorial group theorists are turning out to act properly on CAT(0) cube complexes. This is leading to an increased and more unified understanding of these groups, as well as the resolution of some of the algebraic problems that were first raised in combinatorial group theory but were unapproachable without geometric methods. We will survey groups acting on CAT(0) cube complexes with an eye towards these recent developments.
16:00-16:45 Francisco F. Lasheras, University of Seville, Dpto. Geometria & Topologia, Apdo. 1160, 41080-Sevilla (Spain)
Some open questions on properly 3-realizable groups.
We recall that a finitely presented group is properly 3-realizable if it is the fundamental group of a finite 2-polyhedron whose universal cover has the proper homotopy type of a 3-manifold. We present a quick review of properly 3-realizabler groups and their relation to well-known conjectures and other properties for finitely presented groups such as semistability at infinity and the WGSC and QSF properties.
17:00 - 17:45 Mihai D. Staic, SUNY at Buffalo
Lattice field theory and D-Groups.
We introduce D-groups and show how they fit in the context of lattice field theory. To a manifold M we associate a D-group G(M). We define the symmetric cohomology HSn(G, A) of a group G with coefficients in a G-module A. The D-group G(M) is determined by the action of p1(M) on p2(M) and an element of HS3(p1(M), p2(M)).

Thursday Aug 17

10-11

Zlil Sela, Hebrew University
Diophantine geometry over groups and the elementary theory of a free group

11:15 – 12:15 Jon McCammond, UC Santa Barbara
The geometry of groups defined geometrically
14:30-15:30 Daniel Wise, McGill University
Nonpositively Curved Cube Complexes in Geometric Group Theory
15:45-16:45

Stephen Pride, University of Glasgow
On the residual finiteness and other properties of (relative) one-relator groups
A relative one-relator presentation has the form P = <x, H; R > where x is a set, H is a group, and R is a word on x±1 ?H. We show that if the word on x±1 obtained from R by deleting all the terms from H has what we call the unique max-min property, then the group defined by P is residually finite if and only if H is residually finite. We apply this to obtain new results concerning the residual finiteness of (ordinary) one-relator groups. We also obtain results concerning the conjugacy problem for one-relator groups, and results concerning the relative asphericity of presentations of the form P.

18:30 Dinner

Friday Aug 18

10-11

Zlil Sela, Hebrew University
Diophantine geometry over groups and the elementary theory of a free group

11:15 – 12:15 Jon McCammond, UC Santa Barbara
The geometry of groups defined geometrically
14:30-15:30 Daniel Wise, McGill University
Nonpositively Curved Cube Complexes in Geometric Group Theory
16:00-16:45 Bartosz Putrycz, Institute of Mathematics, University of Gdansk
Commutator subgroups of Hantzsche-Wendt groups.
Let a generalized Hantzsche-Wendt (GHW) group be the fundamental group of a flat n-manifold with holonomy group Z2n-1. Let a Hantzsche-Wendt (HW) group be a GHW group of an orientable manifold (n has to be odd). We prove that for any HW group, with n > 3, its commutator subgroup and translation subgroup are equal, hence its abelianization is Z2n-1. We also give examples of GHW groups with the same property for all n > 4. All these groups are examples of torsion-free metabelian groups with abelianizations Z2k for k > 3.
17:00-17:45

Nicholas Touikan, McGill University
A fast algorithm for Stallings' folding process

Saturday Aug 19

9:30-10:30

Kanta Gupta, University of Manitoba
TBA

11:00-11:45

Volker Diekert, Universität Stuttgart
Coauthors: Markus Lohrey, Alexander Miller
Free partially commutative inverse monoids.
Free partially commutative inverse monoids were first studied in the thesis of da Costa in 2003, where, among others, the word problem has been shown to be decidable.
We give a new approach to define free partially commutative inverse monoids which is closer to standard constructions of Birget - Rhodes and Margolis - Meakin. We use a natural closure operation for subsets of free partially commutative groups - also known as graph groups. We show that the word problem of a free partially commutative inverse monoid is solvable in time O(n log(n)) on a RAM.
The generalized word problem asks whether a given monoid element belongs to a given finitely generated submonoid. In fact, we consider the more general membership problem for rational subsets of a free partially commutative inverse monoid, and we show its NP-completeness. NP-hardness appears already for the special case of the generalized word problem for a 2-generator free inverse monoid. It is quite remarkable that the generalized word problem remains decidable in our setting, because it is known to be undecidable for direct products of free groups. So there is an undecidable problem for a direct product of free groups where the same problem is decidable for a direct product of free inverse monoids.
In the second part of the paper we consider free partially commutative inverse monoids modulo a finite idempotent presentations, which is a finite set of identities between idempotent elements. We show that the resulting quotient monoids have decidable word problems if and only if the underlying dependence structure is transitive. In the transitive case, the uniform word problem (where the idempotent presentation is part of the input) turns out to be EXP-complete, whereas for a fixed idempotent presentation the word problem is solvable both in linear time on a RAM and logarithmic space on a Turing machine.
Our decidability result for the case of a transitive dependence structure is unexpected in light of a result of Meakin and Sapir (1996), where it was shown that there exist E-unitary inverse monoids over a finitely generated Abelian group, where the word problem is undecidable.
The talk is based on a joint work with Markus Lohrey Alexander Miller which appears at MFCS 2006 (proceedings in the Springer LNCS series).

12:00-1:00

Andrzej Szczepanski, University of Gdansk, Poland
Spin structures on flat manifolds
Coauthors: G.Hiss (RWTH, Aachen)
Let G be a torsion free crystallographic group of dimension n such that a flat manifold R^n/G is oriented one. We say that G has a spin structure iff there exist a map e:G --> Spin(n) such that l e = r, where l is a covering map Spin(n)-> SO(n) and r is a holonomy map G --> SO(n). We shall present some conditions for existing (or not) a spin structure on torsion free crystallographic groups. For example for the space groups with point groups of order four. We shall present many examples of Bieberbach groups with and without spin structures.

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