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Eleven papers published by Geometry & Topology Publications
Posted:
Jun 24, 2011 6:00 AM
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Five papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 11 (2011) 1793-1820
Periodic flats in CAT(0) cube complexes
by Michah Sageev and Daniel T Wise
URL: http://www.msp.warwick.ac.uk/agt/2011/11-03/p059.xhtml
DOI: 10.2140/agt.2011.11.1793
(2) Algebraic & Geometric Topology 11 (2011) 1821-1860
Polynomial 6j-symbols and states sums
by Nathan Geer and Bertrand Patureau-Mirand
URL: http://www.msp.warwick.ac.uk/agt/2011/11-03/p060.xhtml
DOI: 10.2140/agt.2011.11.1821
(3) Algebraic & Geometric Topology 11 (2011) 1861-1892
Configuration spaces of thick particles on a metric graph
by Kenneth Deeley
URL: http://www.msp.warwick.ac.uk/agt/2011/11-04/p061.xhtml
DOI: 10.2140/agt.2011.11.1861
(4) Algebraic & Geometric Topology 11 (2011) 1893-1914
Toda brackets and congruences of modular forms
by Gerd Laures
URL: http://www.msp.warwick.ac.uk/agt/2011/11-04/p062.xhtml
DOI: 10.2140/agt.2011.11.1893
(5) Algebraic & Geometric Topology 11 (2011) 1915-1959
The additivity of the rho-invariant and periodicity in topological surgery
by Diarmuid Crowley and Tibor Macko
URL: http://www.msp.warwick.ac.uk/agt/2011/11-04/p063.xhtml
DOI: 10.2140/agt.2011.11.1915
Six papers have been published by Geometry & Topology
(6) Geometry & Topology 15 (2011) 827-890
Realising end invariants by limits of minimally parabolic, geometrically finite groups
by Ken'ichi Ohshika
URL: http://www.msp.warwick.ac.uk/gt/2011/15-02/p023.xhtml
DOI: 10.2140/gt.2011.15.827
(7) Geometry & Topology 15 (2011) 891-925
Topological obstructions to fatness
by Luis A Florit and Wolfgang Ziller
URL: http://www.msp.warwick.ac.uk/gt/2011/15-02/p024.xhtml
DOI: 10.2140/gt.2011.15.891
(8) Geometry & Topology 15 (2011) 927-975
Ricci flow on open 3-manifolds and positive scalar curvature
by Laurent Bessieres, Gerard Besson and Sylvain Maillot
URL: http://www.msp.warwick.ac.uk/gt/2011/15-02/p025.xhtml
DOI: 10.2140/gt.2011.15.927
(9) Geometry & Topology 15 (2011) 977-1012
Trees of cylinders and canonical splittings
by Vincent Guirardel and Gilbert Levitt
URL: http://www.msp.warwick.ac.uk/gt/2011/15-02/p026.xhtml
DOI: 10.2140/gt.2011.15.977
(10) Geometry & Topology 15 (2011) 1013-1027
A Milnor-Wood inequality for complex hyperbolic lattices in quaternionic space
by Oscar Garcia-Prada and Domingo Toledo
URL: http://www.msp.warwick.ac.uk/gt/2011/15-02/p027.xhtml
DOI: 10.2140/gt.2011.15.1013
(11) Geometry & Topology 15 (2011) 1029-1106
An algorithm to determine the Heegaard genus of a 3-manifold
by Tao Li
URL: http://www.msp.warwick.ac.uk/gt/2011/15-02/p028.xhtml
DOI: 10.2140/gt.2011.15.1029
Abstracts follow
(1) Periodic flats in CAT(0) cube complexes
by Michah Sageev and Daniel T Wise
We show that the flat closing conjecture is true for groups acting
properly and cocompactly on a CAT(0) cube complex when the action
satisfies the cyclic facing triple property. For instance, this
property holds for fundamental groups of 3-manifolds that act freely
on CAT(0) cube complexes.
(2) Polynomial 6j-symbols and states sums
by Nathan Geer and Bertrand Patureau-Mirand
For a given 2r-th root of unity xi, we give explicit formulas of a
family of 3--variable Laurent polynomials J_{i,j,k} with coefficients
in Z[qr] that encode the 6j-symbols associated with nilpotent
representations of U_{xi}(sl(2)). For a given abelian group G, we use
them to produce a state sum invariant tau^r(M,L,h_1,h_2) of a
quadruplet (compact 3-manifold M, link L inside M, homology class h_1
in H_1(M,Z), homology class h_2 in H_2(M,G)) with values in a ring R
related to G. The formulas are established by a "skein" calculus as
an application of the theory of modified dimensions introduced by the
authors and Turaev in [Compos. Math. 145 (2009) 196--212]. For an
oriented 3--manifold M, the invariants are related to tau(M,L,phi in
H^1(M,C^*)) defined by the authors and Turaev in [arXiv:0910.1624]
from the category of nilpotent representations of U_{xi}(sl(2)). They
refine them as tau(M,L,phi)= sum_{h_1} tau^r(M,L,h_1,tildephi) where
tildephi correspond to phi with the isomorphism between H_2(M,C^*) and
H^1(M,C^*).
(3) Configuration spaces of thick particles on a metric graph
by Kenneth Deeley
We study the topology of configuration spaces F_r(Gamma,2) of two
thick particles (robots) of radius r>0 moving on a metric graph
Gamma. As the size of the robots increases, the topology of
F_r(Gamma,2) varies. Given Gamma and r, we provide an algorithm for
computing the number of path components of F_r(Gamma,2). Using our
main tool of PL Morse-Bott theory, we show that there are finitely
many critical values of r where the homotopy type of F_r(Gamma,2)
changes. We study the transition across a critical value R in the
interval (a,b) by computing the ranks of the relative homology groups
of (F_a(Gamma,2),F_b(Gamma,2)).
(4) Toda brackets and congruences of modular forms
by Gerd Laures
This paper investigates the relation between Toda brackets and
congruences of modular forms. It determines the f-invariant of Toda
brackets and thereby generalizes the formulas of J F Adams for the
classical e-invariant to the chromatic second filtration.
(5) The additivity of the rho-invariant and periodicity in topological surgery
by Diarmuid Crowley and Tibor Macko
For a closed topological manifold M with dimension at least 5 the
topological structure set S(M) admits an abelian group structure which
may be identified with the algebraic structure group of M as defined
by Ranicki. If the dimension of M is 2d-1, M is oriented and M is
equipped with a map to the classifying space of a finite group G, then
the reduced rho-invariant defines a function from S(M) to a certain
subquotient of the complex representation ring of G. We show that
this function is a homomorphism when 2d-1 is at least 5. Along the
way we give a detailed proof that a geometrically defined map due to
Cappell and Weinberger realises the 8-fold Siebenmann periodicity map
in topological surgery.
(6) Realising end invariants by limits of minimally parabolic, geometrically finite groups
by Ken'ichi Ohshika
We shall show that for a given homeomorphism type and a set of end
invariants (including the parabolic locus) with necessary topological
conditions which a topologically tame Kleinian group with that
homeomorphism type must satisfy, there is an algebraic limit of
minimally parabolic, geometrically finite Kleinian groups which has
exactly that homeomorphism type and the given end invariants. This
shows that the Bers-Sullivan-Thurston density conjecture follows
from Marden's conjecture proved by Agol and Calegari-Gabai combined
with Thurston's uniformisation theorem and the ending lamination
conjecture proved by Minsky, partially collaborating with Masur, Brock
and Canary.
(7) Topological obstructions to fatness
by Luis A Florit and Wolfgang Ziller
Alan Weinstein showed that certain characteristic numbers of any
Riemannian submersion with totally geodesic fibers and positive
vertizontal curvatures are nonzero. In this paper we explicitly
compute these invariants in terms of Chern and Pontrjagin numbers of
the bundle. This allows us to show that many bundles do not admit such
metrics.
(8) Ricci flow on open 3-manifolds and positive scalar curvature
by Laurent Bessieres, Gerard Besson and Sylvain Maillot
We show that an orientable 3-dimensional manifold M admits a complete
riemannian metric of bounded geometry and uniformly positive scalar
curvature if and only if there exists a finite collection F of
spherical space-forms such that M is a (possibly infinite) connected
sum where each summand is diffeomorphic to the product of S^2 x S^1 or
to some member of F. This result generalises G Perelman's
classification theorem for compact 3-manifolds of positive scalar
curvature. The main tool is a variant of Perelman's surgery
construction for Ricci flow.
(9) Trees of cylinders and canonical splittings
by Vincent Guirardel and Gilbert Levitt
Let T be a tree with an action of a finitely generated group G. Given
a suitable equivalence relation on the set of edge stabilizers of T
(such as commensurability, coelementarity in a relatively hyperbolic
group, or commutation in a commutative transitive group), we define a
tree of cylinders T_c. This tree only depends on the deformation space
of T; in particular, it is invariant under automorphisms of G if T is
a JSJ splitting. We thus obtain Out(G)-invariant cyclic or abelian JSJ
splittings. Furthermore, T_c has very strong compatibility properties
(two trees are compatible if they have a common refinement).
(10) A Milnor-Wood inequality for complex hyperbolic lattices in quaternionic space
by Oscar Garcia-Prada and Domingo Toledo
We prove a Milnor-Wood inequality for representations of the
fundamental group of a compact complex hyperbolic manifold in the
group of isometries of quaternionic hyperbolic space. Of special
interest is the case of equality, and its application to rigidity. We
show that equality can only be achieved for totally geodesic
representations, thereby establishing a global rigidity theorem for
totally geodesic representations.
(11) An algorithm to determine the Heegaard genus of a 3-manifold
by Tao Li
We give an algorithmic proof of the theorem that a closed orientable
irreducible and atoroidal 3-manifold has only finitely many Heegaard
splittings in each genus, up to isotopy. The proof gives an algorithm
to determine the Heegaard genus of an atoroidal 3-manifold.
Geometry & Topology Publications is an imprint of
Mathematical Sciences Publishers
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