Three papers published by Geometric & Topology Publications

Geometry and Topology · science forum beginner Joined: 24 May 2006 Posts: 4

** Three papers have been published by Geometry & Topology
Publications

** One papers has been published by Geometry & Topology at
http://msp.warwick.ac.uk/gt/gtcontents10.html

(1) A note on knot Floer homology of links
by Yi Ni

** Two papers have been published by Algebraic & Geometric Topology
at http://msp.warwick.ac.uk/agt/agtcontents6.html

(2) On realizing diagrams of Pi-algebras
by David Blanc, Mark W Johnson and James M Turner

(3) Categorical sequences
by Rob Nendorf, Nick Scoville and Jeff Strom

** Abstracts follow:

(1)
A note on knot Floer homology of links
by
Yi Ni

URL: http://msp.warwick.ac.uk/gt/ftp/main/2006/gt-10-19.pdf

Ozsvath and Szabo proved that knot Floer homology determines
the genera of knots in S^3. We will generalize this deep result
to links in homology 3-spheres, by adapting their method. Our
proof relies on a result of Gabai and some constructions related
to foliations. We also interpret a theorem of Kauffman in the
world of knot Floer homology, hence we can compute the top
filtration term of the knot Floer homology for alternative links.

(2) On realizing diagrams of Pi-algebras
by
David Blanc, Mark W Johnson and James M Turner

URL: http://msp.warwick.ac.uk/agt/ftp/main/2006/agt-06-29.pdf

Given a diagram of Pi-algebras (graded groups equipped with an action
of the primary homotopy operations), we ask whether it can be realized
as the homotopy groups of a diagram of spaces. The answer given here
is in the form of an obstruction theory, of somewhat wider
application, formulated in terms of generalized Pi-algebras. This
extends a program begun in [J. Pure Appl. Alg. 103 (1995) 167-188] and
[Topology 43 (2004) 857-892] to study the realization of a single
Pi-algebra. In particular, we explicitly analyze the simple case of a
single map, and provide a detailed example, illustrating the
connections to higher homotopy operations.

(3) Categorical sequences
by
Rob Nendorf, Nick Scoville and Jeff Strom

URL: http://msp.warwick.ac.uk/agt/ftp/main/2006/agt-06-30.pdf

We define and study the categorical sequence of a space, which is a
new formalism that streamlines the computation of the
Lusternik-Schnirelmann category of a space X by induction on its CW
skeleta. The k-th term in the categorical sequence of a CW complex X,
\sigma_X(k), is the least integer n for which cat_X(X_n) >= k. We
show that \sigma_X is a well-defined homotopy invariant of X.

We prove that \sigma_X(k+l) >= \sigma_X(k) + \sigma_X(l), which is one
of three keys to the power of categorical sequences. In addition to
this formula, we provide formulas relating the categorical sequences
of spaces and some of their algebraic invariants, including their
cohomology algebras and their rational models; we also find relations
between the categorical sequences of the spaces in a fibration
sequence and give a preliminary result on the categorical sequence of
a product of two spaces in the rational case. We completely
characterize the sequences which can arise as categorical sequences of
formal rational spaces. The most important of the many examples that
we offer is a simple proof of a theorem of Ghienne: if X is a member
of the Mislin genus of the Lie group Sp(3), then cat(X) = cat(Sp(3)).

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