Five papers published by Geometric & Topology Publications

Geometry and Topology · science forum beginner Joined: 24 May 2006 Posts: 4

Geometry & Topology Publications have published five papers. Three
are published by Geometry & Topology and two by Algebraic & Geometric
Topology.

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Published by Geometry & Topology at
http://www.maths.warwick.ac.uk/gt/gtcontents10.html

(1) Dynamics of the mapping class group action on the variety of
PSL_2(C) characters
by Juan Souto and Peter Storm

(2) Infinitely many hyperbolic Coxeter groups through dimension 19
by Daniel Allcock

(3) The integral cohomology of the group of loops
by Craig Jensen, Jon McCammond and John Meier

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Published by Algebraic & Geometric Topology at
http://www.maths.warwick.ac.uk/agt/agtcontents6.html

(4) A geometric proof that SL_2(Z[t,t^{-1}]) is not
finitely presented
by Kai-Uwe Bux and Kevin Wortman

(5) Heegaard splittings and the pants complex
by Jesse Johnson

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Abstracts and URL's follow:

(1) Dynamics of the mapping class group action on the variety of
PSL_2(C) characters
by Juan Souto and Peter Storm

http://msp.warwick.ac.uk/gt/ftp/main/2006/gt-10-20.pdf

We study the action of the mapping class group Mod(S) on the boundary dQ
of quasifuchsian space Q. Among other results, Mod(S) is shown to be
topologically transitive on the subset C in dQ of manifolds without a
conformally compact end. We also prove that any open subset of the
character variety X(pi_1(S),SL(2,C)) intersecting dQ does not admit a
nonconstant Mod(S)-invariant meromorphic function. This is related to a
question of Goldman.

(2) Infinitely many hyperbolic Coxeter groups through dimension 19
by Daniel Allcock

http://msp.warwick.ac.uk/gt/ftp/main/2006/gt-10-21.pdf

We prove the following: there are infinitely many finite-covolume
(resp. cocompact) Coxeter groups acting on hyperbolic space H^n for
every n < 20 (resp. n < 7). When n=7 or 8, they may be taken to be
nonarithmetic. Furthermore, for 1 < n < 20, with the possible
exceptions n=16 and 17, the number of essentially distinct Coxeter
groups in H^n with noncompact fundamental domain of volume less than
or equal to V grows at least exponentially with respect to V. The
same result holds for cocompact groups for n < 7. The technique is a
doubling trick and variations on it; getting the most out of the
method requires some work with the Leech lattice.

(3) The integral cohomology of the group of loops
by Craig Jensen, Jon McCammond and John Meier

http://msp.warwick.ac.uk/gt/ftp/main/2006/gt-10-22.pdf

Let PSigma_n denote the group that can be thought of either as the
group of motions of the trivial n-component link or the group of
symmetric automorphisms of a free group of rank n. The integral
cohomology ring of PSigma_n is determined, establishing a conjecture
of Brownstein and Lee.

(4) A geometric proof that SL_2(Z[t,t^{-1}]) is not
finitely presented
by Kai-Uwe Bux and Kevin Wortman

http://msp.warwick.ac.uk/agt/ftp/main/2006/gt-06-31.pdf

We give a new proof of the theorem of Krstic-McCool from
the title. Our proof has potential applications to the study of
finiteness properties of other subgroups of SL_2 resulting
from rings of functions on curves.

(5) Heegaard splittings and the pants complex
by Jesse Johnson

http://msp.warwick.ac.uk/agt/ftp/main/2006/gt-06-32.pdf

We define integral measures of complexity for Heegaard splittings based on the
graph dual to the curve complex and on the pants complex defined by Hatcher
and Thurston. As the Heegaard splitting is stabilized, the sequence of
complexities turns out to converge to a non-trivial limit depending only on the
manifold. We then use a similar method to compare different manifolds,
defining a distance which converges under stabilization to an integer related
to Dehn surgeries between the two manifolds.

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