geometry and topology

Four papers have been published by Algebraic and Geometric Topology

(1) Algebraic & Geometric Topology 6 (2006) 1429-1457
Holomorphic discs and sutured manifolds
by Andras Juhasz
URL: http://www.msp.warwick.ac.uk/agt/2006/06/p052.xhtml
DOI: 10.2140/agt.2006.6.1429

(2) Algebraic & Geometric Topology 6 (2006) 1459-1469
The Karoubi envelope and Lee's degeneration of Khovanov homology
by Dror Bar-Natan and Scott Morrison
URL: http://www.msp.warwick.ac.uk/agt/2006/06/p053.xhtml
DOI: 10.2140/agt.2006.6.1459

(3) Algebraic & Geometric Topology 6 (2006) 1471-1489
Cohomology of preimages with local coefficients
by Daciberg Goncalves and Peter Wong
URL: http://www.msp.warwick.ac.uk/agt/2006/06/p054.xhtml
DOI: 10.2140/agt.2006.6.1471

(4) Algebraic & Geometric Topology 6 (2006) 1491-1517
Cosmetic surgeries on genus one knots
by Jiajun Wang
URL: http://www.msp.warwick.ac.uk/agt/2006/06/p055.xhtml
DOI: 10.2140/agt.2006.6.1491

Three papers have been published by Geometry and Topology

(5) Geometry & Topology 10 (2006) 1373-1389
Dense embeddings of surface groups
by Emmanuel Breuillard, Tsachik Gelander, Juan Souto and Peter Storm
URL: http://www.msp.warwick.ac.uk/gt/2006/10/p034.xhtml
DOI: 10.2140/gt.2006.10.1373

(6) Geometry & Topology 10 (2006) 1391-1424
On the chain-level intersection pairing for PL manifolds
by J E McClure
URL: http://www.msp.warwick.ac.uk/gt/2006/10/p035.xhtml
DOI: 10.2140/gt.2006.10.1391

(7) Geometry & Topology 10 (2006) 1425-1452
Stabilization in the braid groups II: Transversal simplicity of knots
by Joan S Birman and William W Menasco
URL: http://www.msp.warwick.ac.uk/gt/2006/10/p036.xhtml
DOI: 10.2140/gt.2006.10.1425

Abstracts follow

(1) Holomorphic discs and sutured manifolds
by Andras Juhasz

In this paper we construct a Floer-homology invariant for a natural
and wide class of sutured manifolds that we call balanced. This
generalizes the Heegaard Floer hat theory of closed three-manifolds
and links. Our invariant is unchanged under product decompositions
and is zero for nontaut sutured manifolds. As an application, an
invariant of Seifert surfaces is given and is computed in a few
interesting cases.


(2) The Karoubi envelope and Lee's degeneration of Khovanov homology
by Dror Bar-Natan and Scott Morrison

We give a simple proof of Lee's result from [Adv. Math. 179 (2005)
554-586], that the dimension of the Lee variant of the Khovanov
homology of a c-component link is 2^c, regardless of the number of
crossings. Our method of proof is entirely local and hence we can
state a Lee-type theorem for tangles as well as for knots and
links. Our main tool is the ``Karoubi envelope of the cobordism
category'', a certain enlargement of the cobordism category which is
mild enough so that no information is lost yet strong enough to allow
for some simplifications that are otherwise unavailable.


(3) Cohomology of preimages with local coefficients
by Daciberg Goncalves and Peter Wong

Let M,N and B\subset N be compact smooth manifolds of dimensions n+k,n
and \ell, respectively. Given a map f from M to N, we give homological
conditions under which g^{-1}(B) has nontrivial cohomology (with local
coefficients) for any map g homotopic to f. We also show that a
certain cohomology class in H^j(N,N-B) is Poincare dual (with local
coefficients) under f^* to the image of a corresponding class in
H_{n+k-j}(f^{-1}(B)) when f is transverse to B. This generalizes a
similar formula of D\,Gottlieb in the case of simple coefficients.


(4) Cosmetic surgeries on genus one knots
by Jiajun Wang

In this paper, we prove that there are no truly cosmetic surgeries
on genus one classical knots. If the two surgery slopes have the same sign,
we give the only possibilities of reflectively cosmetic surgeries. The result
is an application of Heegaard Floer theory and number theory.


(5) Dense embeddings of surface groups
by Emmanuel Breuillard, Tsachik Gelander, Juan Souto and Peter Storm

We discuss dense embeddings of surface groups and fully residually
free groups in topological groups. We show that a compact topological
group contains a nonabelian dense free group of finite rank if and
only if it contains a dense surface group. Also, we obtain a
characterization of those Lie groups which admit a dense faithfully
embedded surface group. Similarly, we show that any connected
semisimple Lie group contains a dense copy of any fully residually
free group.


(6) On the chain-level intersection pairing for PL manifolds
by J E McClure

Let M be a compact oriented PL manifold and let C_*M be its PL
chain complex. The domain of the chain-level intersection pairing is a
subcomplex G of C_*M\otimes C_*M. We prove that G is a ``full''
subcomplex, that is, the inclusion of G in C_*M \otimes C_*M is a
quasi-isomorphism. An ****ogous result is true for the domain of the
iterated intersection pairing. Using this, we show that the intersection
pairing gives C_*M a structure of partially defined commutative DGA, which
in particular implies that C_*M is canonically quasi-isomorphic to an
E_\infty chain algebra.


(7) Stabilization in the braid groups II: Transversal simplicity of knots
by Joan S Birman and William W Menasco

The main result of this paper is a negative answer to the question:
are all transversal knot types transversally simple? An ********
infinite family of examples is given of closed 3-braids that define
transversal knot types that are not transversally simple. The method
of proof is topological and indirect.