Nine papers published by Geometry & Topology Publications
Geometry and Topology
(1) Algebraic & Geometric Topology 10 (2010) 525-530
Faithfulness of a functor of Quillen
by William G Dwyer, Andrei Radulescu-Banu and Sebastian Thomas
URL: http://www.msp.warwick.ac.uk/agt/2010/10-01/p015.xhtml
DOI: 10.2140/agt.2010.10.525
(2) Algebraic & Geometric Topology 10 (2010) 531-533
Correction to: "Topological nonrealization results via the
Goodwillie tower approach to iterated loopspace homology"
by Nicholas Kuhn
URL: http://www.msp.warwick.ac.uk/agt/2010/10-01/p016.xhtml
DOI: 10.2140/agt.2010.10.531
(3) Algebraic & Geometric Topology 10 (2010) 535-564
Odd primary homotopy decompositions of gauge groups
by Stephen D Theriault
URL: http://www.msp.warwick.ac.uk/agt/2010/10-01/p017.xhtml
DOI: 10.2140/agt.2010.10.535
(4) Algebraic & Geometric Topology 10 (2010) 565-625
On homotopy groups of the suspended classifying spaces
by Roman Mikhailov and Jie Wu
URL: http://www.msp.warwick.ac.uk/agt/2010/10-01/p018.xhtml
DOI: 10.2140/agt.2010.10.565
(5) Algebraic & Geometric Topology 10 (2010) 627-635
On the tunnel number and the Morse-Novikov number of knots
by Andrei Pajitnov
URL: http://www.msp.warwick.ac.uk/agt/2010/10-02/p019.xhtml
DOI: 10.2140/agt.2010.10.627
(6) Algebraic & Geometric Topology 10 (2010) 637-661
The length of unknotting tunnels
by Daryl Cooper, Marc Lackenby and Jessica S Purcell
URL: http://www.msp.warwick.ac.uk/agt/2010/10-02/p020.xhtml
DOI: 10.2140/agt.2010.10.637
(7) Algebraic & Geometric Topology 10 (2010) 663-677
Commensurability classes containing three knot complements
by Neil Hoffman
URL: http://www.msp.warwick.ac.uk/agt/2010/10-02/p021.xhtml
DOI: 10.2140/agt.2010.10.663
Two papers have been published by Geometry & Topology
(8) Geometry & Topology 14 (2010) 833-902
Quilted Floer cohomology
by Katrin Wehrheim and Chris T Woodward
URL: http://www.msp.warwick.ac.uk/gt/2010/14-02/p020.xhtml
DOI: 10.2140/gt.2010.14.833
(9) Geometry & Topology 14 (2010) 903-966
An index theorem in differential K-theory
by Daniel S Freed and John Lott
URL: http://www.msp.warwick.ac.uk/gt/2010/14-02/p021.xhtml
DOI: 10.2140/gt.2010.14.903
Abstracts follow
(1) Faithfulness of a functor of Quillen
by William G Dwyer, Andrei Radulescu-Banu and Sebastian Thomas
There exists a canonical functor from the category of fibrant objects
of a model category modulo cylinder homotopy to its homotopy
category. We show that this functor is faithful under certain
conditions, but not in general.
(2) Correction to: "Topological nonrealization results via the
Goodwillie tower approach to iterated loopspace homology"
by Nicholas Kuhn
Manfred Stelzer has pointed out that part of Corollary 4.5 of
[Algebr. Geom. Topol. 8 (2008) 2109-2129] was not sufficiently proved,
and, indeed, is likely incorrect as stated. This necessitates a
little more argument to finish the proof of the main theorem of that
paper. The statement of this theorem, and all the examples, remain
unchanged.
(3) Odd primary homotopy decompositions of gauge groups
by Stephen D Theriault
We construct p-local decompositions of certain gauge groups when p is
an odd prime. Specifically, we decompose SU(n), Sp(n) and
Spin(n)-gauge groups over simply connected 4-manifolds and U(n)-gauge
groups over compact, orientable Riemann surfaces, given certain
restrictions on n that depend on p.
(4) On homotopy groups of the suspended classifying spaces
by Roman Mikhailov and Jie Wu
In this paper, we determine the homotopy groups pi_4(Sigma K(A,1)) and
pi_5(Sigma K(A,1)) for abelian groups A by using the following methods
from group theory and homotopy theory: derived functors, the Carlsson
simplicial construction, the Baues--Goerss spectral sequence, homotopy
decompositions and the methods of algebraic $K$--theory. As the
applications, we also determine pi_i(Sigma K(G,1)) with i=4,5 for some
nonabelian groups G=Sigma_3 and SL(Z) and pi_4(Sigma K(A_4,1)) for the
4-th alternating group A_4.
(5) On the tunnel number and the Morse-Novikov number of knots
by Andrei Pajitnov
Let L be a link in S^3; denote by MN(L) the Morse-Novikov number of L
and by t(L) the tunnel number of L. We prove that MN(L) <= 2t(L) and
deduce several corollaries.
(6) The length of unknotting tunnels
by Daryl Cooper, Marc Lackenby and Jessica S Purcell
We show there exist tunnel number one hyperbolic 3-manifolds with
arbitrarily long unknotting tunnel. This provides a negative answer
to an old question of Colin Adams.
(7) Commensurability classes containing three knot complements
by Neil Hoffman
This paper exhibits an infinite family of hyperbolic knot complements
that have three knot complements in their respective commensurability
classes.
(8) Quilted Floer cohomology
by Katrin Wehrheim and Chris T Woodward
We generalize Lagrangian Floer cohomology to sequences of Lagrangian
correspondences. For sequences related by the geometric composition of
Lagrangian correspondences we establish an isomorphism of the Floer
cohomologies. This provides the foundation for the construction of a
symplectic 2-category as well as for the definition of topological
invariants via decomposition and representation in the symplectic
category. Here we give some first direct symplectic applications:
Calculations of Floer cohomology, displaceability of Lagrangian
correspondences and transfer of displaceability under geometric
composition.
(9) An index theorem in differential K-theory
by Daniel S Freed and John Lott
Let pi: X --> B be a proper submersion with a Riemannian structure.
Given a differential K-theory class on X, we define its analytic and
topological indices as differential K-theory classes on B. We prove
that the two indices are the same.