Completion of publication in 2010 of GT and AGT
Geometry and Topology
of Volume 14 (2010) of GT and of Volume 10 (2010) of AGT.
Volume 14 of GT finishes with an issue (number 5) devoted to a set of
five papers by Cliff Taubes which construct an isomorphism between the
embedded contact homology and Seiberg-Witten Floer cohomology of a
compact 3-manifold with a given contact 1-form. These are papers 7 to
11.
Papers 1 to 4 complete the final issue (number 4) of AGT Volume 10 and
papers 5 to 6 complete the penultimate issue (number 4) of GT Volume 14.
The four papers published by Algebraic & Geometric Topology are:
(1) Algebraic & Geometric Topology 10 (2010) 2343-2408
Symmetric homology of algebras
by Shaun V Ault
URL: http://www.msp.warwick.ac.uk/agt/2010/10-04/p079.xhtml
DOI: 10.2140/agt.2010.10.2343
(2) Algebraic & Geometric Topology 10 (2010) 2409-2418
On free discrete subgroups of Diff(I)
by Azer Akhmedov
URL: http://www.msp.warwick.ac.uk/agt/2010/10-04/p080.xhtml
DOI: 10.2140/agt.2010.10.2409
(3) Algebraic & Geometric Topology 10 (2010) 2419-2450
The general notion of descent in coarse geometry
by Paul D Mitchener
URL: http://www.msp.warwick.ac.uk/agt/2010/10-04/p081.xhtml
DOI: 10.2140/agt.2010.10.2419
(4) Algebraic & Geometric Topology 10 (2010) 2451-2468
Divergence et parallelisme des rayons d'etirement cylindriques
by Guillaume Théret
URL: http://www.msp.warwick.ac.uk/agt/2010/10-04/p082.xhtml
DOI: 10.2140/agt.2010.10.2451
The two papers published by Geometry & Topology in Issue 4 are:
(5) Geometry & Topology 14 (2010) 2431-2477
Algebraic and geometric convergence of discrete representations into PSL_2C
by Ian Biringer and Juan Souto
URL: http://www.msp.warwick.ac.uk/gt/2010/14-04/p054.xhtml
DOI: 10.2140/gt.2010.14.2431
(6) Geometry & Topology 14 (2010) 2479-2496
Describing the universal cover of a noncompact limit
by John Ennis and Guofang Wei
URL: http://www.msp.warwick.ac.uk/gt/2010/14-04/p055.xhtml
DOI: 10.2140/gt.2010.14.2479
The set of five papers published by Geometry & Topology as Issue 5 are:
(7) Geometry & Topology 14 (2010) 2497-2581
Embedded contact homology and Seiberg-Witten Floer cohomology I
by Clifford Henry Taubes
URL: http://www.msp.warwick.ac.uk/gt/2010/14-05/p056.xhtml
DOI: 10.2140/gt.2010.14.2497
(8) Geometry & Topology 14 (2010) 2583-2720
Embedded contact homology and Seiberg-Witten Floer cohomology II
by Clifford Henry Taubes
URL: http://www.msp.warwick.ac.uk/gt/2010/14-05/p057.xhtml
DOI: 10.2140/gt.2010.14.2583
(9) Geometry & Topology 14 (2010) 2721-2817
Embedded contact homology and Seiberg-Witten Floer cohomology III
by Clifford Henry Taubes
URL: http://www.msp.warwick.ac.uk/gt/2010/14-05/p058.xhtml
DOI: 10.2140/gt.2010.14.2721
(10) Geometry & Topology 14 (2010) 2819-2960
Embedded contact homology and Seiberg-Witten Floer cohomology IV
by Clifford Henry Taubes
URL: http://www.msp.warwick.ac.uk/gt/2010/14-05/p059.xhtml
DOI: 10.2140/gt.2010.14.2819
(11) Geometry & Topology 14 (2010) 2961-3000
Embedded contact homology and Seiberg-Witten Floer cohomology V
by Clifford Henry Taubes
URL: http://www.msp.warwick.ac.uk/gt/2010/14-05/p060.xhtml
DOI: 10.2140/gt.2010.14.2961
Abstracts follow
(1) Symmetric homology of algebras
by Shaun V Ault
The symmetric homology of a unital algebra A over a commutative ground
ring k is defined using derived functors and the symmetric bar
construction of Fiedorowicz. For a group ring A = k[Gamma], the
symmetric homology is related to stable homotopy theory via
HS_*(k[Gamma]) cong H_*(Omega Omega^{infty} S^{infty}(BGamma); k).
Two chain complexes that compute HS_*(A) are constructed, both making
use of a symmetric monoidal category Delta S_+ containing Delta S.
Two spectral sequences are found that aid in computing symmetric
homology. The second spectral sequence is defined in terms of a
family of complexes, Sym^(p)_*. Sym^(p) is isomorphic to the
suspension of the cycle-free chessboard complex Omega_{p+1} of Vrecica
and Zivaljevic, and so recent results on the connectivity of Omega_n
imply finite-dimensionality of the symmetric homology groups of
finite-dimensional algebras. Some results about the k
Sigma_{p+1}-module structure of Sym^(p) are devloped. A partial
resolution is found that allows computation of HS_1(A) for
finite-dimensional A and some concrete computations are included.
(2) On free discrete subgroups of Diff(I)
by Azer Akhmedov
We prove that the free group F_2 admits a faithful discrete
representation into Diff_+^1 [0,1]. We also prove that F_2 admits a
faithful discrete representation of bi-Lipschitz class into
Homeo_+[0,1]. Some properties of these representations are studied.
(3) The general notion of descent in coarse geometry
by Paul D Mitchener
In this article, we introduce the notion of a functor on coarse spaces
being "coarsely excisive" - a coarse analogue of the notion of a
functor on topological spaces being excisive. Further, taking cones,
a coarsely excisive functor yields a topologically excisive functor,
and for coarse topological spaces there is an associated coarse
assembly map from the topologically excisive functor to the coarsely
excisive functor.
We conjecture that this coarse assembly map is an isomorphism for
uniformly contractible spaces with bounded geometry, and show that the
coarse isomorphism conjecture, along with some mild technical
conditions, implies that a corresponding equivariant assembly map is
injective. Particular instances of this equivariant assembly map are
the maps in the Farrell-Jones conjecture, and in the Baum-Connes
conjecture.
(4) Divergence et parallelisme des rayons d'etirement cylindriques
by Guillaume Theret
Une ligne d'etirement cylindrique est une ligne d'etirement au sens de
Thurston dont la lamination horocyclique est une multicourbe ponderee.
Nous montrons ici que deux lignes cylindriques correctement
parametrees sont paralleles si et seulement si ces lignes convergent
vers le meme point du bord de Thurston de l'espace de Teichmuller.
A cylindrical stretch line is a stretch line, in the sense of
Thurston, whose horocyclic lamination is a weighted multicurve. In
this paper, we show that two correctly parameterized cylindrical lines
are parallel if and only if these lines converge towards the same
point in Thurston's boundary of Teichmuller space.
(5) Algebraic and geometric convergence of discrete representations into PSL_2C
by Ian Biringer and Juan Souto
Anderson and Canary have shown that if the algebraic limit of a
sequence of discrete, faithful representations of a finitely generated
group into PSL(2,C) does not contain parabolics, then it is also the
sequence's geometric limit. We construct examples that demonstrate the
failure of this theorem for certain sequences of unfaithful
representations, and offer a suitable replacement.
(6) Describing the universal cover of a noncompact limit
by John Ennis and Guofang Wei
Suppose that X is the Gromov--Hausdorff limit of a sequence of
Riemannian manifolds M^n_i with a uniform lower bound on Ricci
curvature. In a previous paper the authors showed that when X is
compact the universal cover tilde{X} is a quotient of the
Gromov--Hausdorff limit of the universal covers tilde{M}^n_i. This is
not true when X is noncompact. In this paper we introduce the notion
of pseudo-nullhomotopic loops and give a description of the universal
cover of a noncompact limit space in terms of the covering spaces of
balls of increasing size in the sequence.
(7-11) Embedded contact homology and Seiberg-Witten Floer cohomology I-V
by Clifford Henry Taubes
Any given oriented, compact 3-dimensional manifold has a number of
associated Floer homologies. One of these is the Seiberg-Witten Floer
homology - also known as Monopole Floer homology. This Floer homology
is computed using an algebraic count of certain pairs of connection
and spinor on the 3-manifold. A second and very different looking
Floer homology is Michael Hutching's embedded contact homology. The
definition of the latter requires the introduction of a contact
structure on the three manifold. This version is computed using an
algebraic count of the closed integral curves of the associated Reeb
vector field. The papers in this issue supply an isomorphism between
embedded contact homology and the Seiberg-Witten Floer cohomology.
This is the first of five papers that construct an isomorphism between
the embedded contact homology and Seiberg--Witten Floer cohomology of
a compact 3-manifold with a given contact 1-form.
Paper I describes what is involved in the construction. Paper II-IV
contain the details of the construction and paper V is a sequel which
proves that the isomorphism that is constructed in the first four
papers is compatible with additional structure carried by the two
cohomology/homology theories under consideration.
Geometry & Topology Publications is an imprint of
Mathematical Sciences Publishers