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Eleven papers published by Geometry & Topology Publications
Posted:
Jun 24, 2011 6:00 AM


Five papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 11 (2011) 17931820 Periodic flats in CAT(0) cube complexes by Michah Sageev and Daniel T Wise URL: http://www.msp.warwick.ac.uk/agt/2011/1103/p059.xhtml DOI: 10.2140/agt.2011.11.1793
(2) Algebraic & Geometric Topology 11 (2011) 18211860 Polynomial 6jsymbols and states sums by Nathan Geer and Bertrand PatureauMirand URL: http://www.msp.warwick.ac.uk/agt/2011/1103/p060.xhtml DOI: 10.2140/agt.2011.11.1821
(3) Algebraic & Geometric Topology 11 (2011) 18611892 Configuration spaces of thick particles on a metric graph by Kenneth Deeley URL: http://www.msp.warwick.ac.uk/agt/2011/1104/p061.xhtml DOI: 10.2140/agt.2011.11.1861
(4) Algebraic & Geometric Topology 11 (2011) 18931914 Toda brackets and congruences of modular forms by Gerd Laures URL: http://www.msp.warwick.ac.uk/agt/2011/1104/p062.xhtml DOI: 10.2140/agt.2011.11.1893
(5) Algebraic & Geometric Topology 11 (2011) 19151959 The additivity of the rhoinvariant and periodicity in topological surgery by Diarmuid Crowley and Tibor Macko URL: http://www.msp.warwick.ac.uk/agt/2011/1104/p063.xhtml DOI: 10.2140/agt.2011.11.1915
Six papers have been published by Geometry & Topology
(6) Geometry & Topology 15 (2011) 827890 Realising end invariants by limits of minimally parabolic, geometrically finite groups by Ken'ichi Ohshika URL: http://www.msp.warwick.ac.uk/gt/2011/1502/p023.xhtml DOI: 10.2140/gt.2011.15.827
(7) Geometry & Topology 15 (2011) 891925 Topological obstructions to fatness by Luis A Florit and Wolfgang Ziller URL: http://www.msp.warwick.ac.uk/gt/2011/1502/p024.xhtml DOI: 10.2140/gt.2011.15.891
(8) Geometry & Topology 15 (2011) 927975 Ricci flow on open 3manifolds and positive scalar curvature by Laurent Bessieres, Gerard Besson and Sylvain Maillot URL: http://www.msp.warwick.ac.uk/gt/2011/1502/p025.xhtml DOI: 10.2140/gt.2011.15.927
(9) Geometry & Topology 15 (2011) 9771012 Trees of cylinders and canonical splittings by Vincent Guirardel and Gilbert Levitt URL: http://www.msp.warwick.ac.uk/gt/2011/1502/p026.xhtml DOI: 10.2140/gt.2011.15.977
(10) Geometry & Topology 15 (2011) 10131027 A MilnorWood inequality for complex hyperbolic lattices in quaternionic space by Oscar GarciaPrada and Domingo Toledo URL: http://www.msp.warwick.ac.uk/gt/2011/1502/p027.xhtml DOI: 10.2140/gt.2011.15.1013
(11) Geometry & Topology 15 (2011) 10291106 An algorithm to determine the Heegaard genus of a 3manifold by Tao Li URL: http://www.msp.warwick.ac.uk/gt/2011/1502/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 3manifolds that act freely on CAT(0) cube complexes.
(2) Polynomial 6jsymbols and states sums by Nathan Geer and Bertrand PatureauMirand
For a given 2rth root of unity xi, we give explicit formulas of a family of 3variable Laurent polynomials J_{i,j,k} with coefficients in Z[qr] that encode the 6jsymbols 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 3manifold 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) 196212]. For an oriented 3manifold 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 MorseBott 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 finvariant of Toda brackets and thereby generalizes the formulas of J F Adams for the classical einvariant to the chromatic second filtration.
(5) The additivity of the rhoinvariant 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 2d1, M is oriented and M is equipped with a map to the classifying space of a finite group G, then the reduced rhoinvariant 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 2d1 is at least 5. Along the way we give a detailed proof that a geometrically defined map due to Cappell and Weinberger realises the 8fold 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 BersSullivanThurston density conjecture follows from Marden's conjecture proved by Agol and CalegariGabai 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 3manifolds and positive scalar curvature by Laurent Bessieres, Gerard Besson and Sylvain Maillot
We show that an orientable 3dimensional 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 spaceforms 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 3manifolds 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 MilnorWood inequality for complex hyperbolic lattices in quaternionic space by Oscar GarciaPrada and Domingo Toledo We prove a MilnorWood 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 3manifold by Tao Li
We give an algorithmic proof of the theorem that a closed orientable irreducible and atoroidal 3manifold 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 3manifold.
Geometry & Topology Publications is an imprint of Mathematical Sciences Publishers



