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Topic: Eleven papers published by Geometry & Topology Publications
Replies: 1   Last Post: May 3, 2013 9:31 PM

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Geometry and Topology

Posts: 140
Registered: 5/24/06
Eleven papers published by Geometry & Topology Publications
Posted: May 3, 2013 9:31 PM
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Nine papers have been published by Algebraic & Geometric Topology,
completing Issue 2 of Volume 13

(1) Algebraic & Geometric Topology 13 (2013) 1049-1051
A streamlined proof of Goodwillie's n-excisive approximation
by Charles Rezk
URL: http://www.msp.warwick.ac.uk/agt/2013/13-02/p032.xhtml
DOI: 10.2140/agt.2013.13.1049

(2) Algebraic & Geometric Topology 13 (2013) 1053-1070
Unstable splittings for real spectra
by Nitu Kitchloo and W Stephen Wilson
URL: http://www.msp.warwick.ac.uk/agt/2013/13-02/p033.xhtml
DOI: 10.2140/agt.2013.13.1053

(3) Algebraic & Geometric Topology 13 (2013) 1071-1087
On the geometric realization and subdivisions of dihedral sets
by Sho Saito
URL: http://www.msp.warwick.ac.uk/agt/2013/13-02/p034.xhtml
DOI: 10.2140/agt.2013.13.1071

(4) Algebraic & Geometric Topology 13 (2013) 1089-1124
On the construction of functorial factorizations for model categories
by Tobias Barthel and Emily Riehl
URL: http://www.msp.warwick.ac.uk/agt/2013/13-02/p035.xhtml
DOI: 10.2140/agt.2013.13.1089

(5) Algebraic & Geometric Topology 13 (2013) 1125-1141
Bridge number and tangle products
by Ryan Blair
URL: http://www.msp.warwick.ac.uk/agt/2013/13-02/p036.xhtml
DOI: 10.2140/agt.2013.13.1125

(6) Algebraic & Geometric Topology 13 (2013) 1143-1159
Nonseparating spheres and twisted Heegaard Floer homology
by Yi Ni
URL: http://www.msp.warwick.ac.uk/agt/2013/13-02/p037.xhtml
DOI: 10.2140/agt.2013.13.1143

(7) Algebraic & Geometric Topology 13 (2013) 1161-1182
Cosimplicial models for the limit of the Goodwillie tower
by Rosona Eldred
URL: http://www.msp.warwick.ac.uk/agt/2013/13-02/p038.xhtml
DOI: 10.2140/agt.2013.13.1161

(8) Algebraic & Geometric Topology 13 (2013) 1183-1224
Homology of moduli spaces of linkages in high-dimensional Euclidean space
by Dirk Schuetz
URL: http://www.msp.warwick.ac.uk/agt/2013/13-02/p039.xhtml
DOI: 10.2140/agt.2013.13.1183

(9) Algebraic & Geometric Topology 13 (2013) 1225-1241
The Kunneth Theorem in equivariant K-theory
for actions of a cyclic group of order 2
by Jonathan Rosenberg
URL: http://www.msp.warwick.ac.uk/agt/2013/13-02/p040.xhtml
DOI: 10.2140/agt.2013.13.1225

Two papers have been published by Geometry & Topology

(10) Geometry & Topology 17 (2013) 639-731
Parametrized ring-spectra and the nearby Lagrangian conjecture
by Thomas Kragh
Appendix: Mohammed Abouzaid
URL: http://www.msp.warwick.ac.uk/gt/2013/17-02/p018.xhtml
DOI: 10.2140/gt.2013.17.639

(11) Geometry & Topology 17 (2013) 733-838
A universal characterization of higher algebraic K-theory
by Andrew Blumberg, David Gepner and Goncalo Tabuada
URL: http://www.msp.warwick.ac.uk/gt/2013/17-02/p019.xhtml
DOI: 10.2140/gt.2013.17.733


Abstracts follow

(1) A streamlined proof of Goodwillie's n-excisive approximation
by Charles Rezk

We give a shorter proof of Goodwillie's, [Geom. Topol. 7 (2003)
645--711; Lemma 1.9], which is the key step in proving that the
construction P_n F gives an n-excisive functor.


(2) Unstable splittings for real spectra
by Nitu Kitchloo and W Stephen Wilson

We show that the unstable splittings of the spaces in the Omega
spectra representing BP, BP<n> and E(n) from [Amer. J. Math. 97 (1975)
101--123] may be obtained for the real analogs of these spectra using
techniques similar to those in [Progr. Math. 196 (2001) 35--45].
Explicit calculations for ER(2) are given.


(3) On the geometric realization and subdivisions of dihedral sets
by Sho Saito

We extend to dihedral sets Drinfeld's filtered-colimit expressions of
the geometric realization of simplicial and cyclic sets. We prove
that the group of homeomorphisms of the circle continuously act on the
geometric realization of a dihedral set. We also see how these
expressions of geometric realization clarify subdivision operations on
simplicial, cyclic and dihedral sets defined by Boekstedt, Hsiang and
Madsen, and Spalinski.


(4) On the construction of functorial factorizations for model categories
by Tobias Barthel and Emily Riehl

We present general techniques for constructing functorial
factorizations appropriate for model structures that are not known to
be cofibrantly generated. Our methods use `algebraic'
characterizations of fibrations to produce factorizations that have
the desired lifting properties in a completely categorical fashion. We
illustrate these methods in the case of categories enriched, tensored
and cotensored in spaces, proving the existence of Hurewicz-type model
structures, thereby correcting an error in earlier attempts by others.
Examples include the categories of (based) spaces, (based) G-spaces
and diagram spectra among others.


(5) Bridge number and tangle products
by Ryan Blair

We show that essential punctured spheres in the complement of links
with distance three or greater bridge spheres have bounded complexity.
We define the operation of tangle product, a generalization of both
connected sum and Conway product. Finally, we use the bounded
complexity of essential punctured spheres to show that the bridge
number of a tangle product is at least the sum of the bridge numbers
of the two factor links up to a constant error.


(6) Nonseparating spheres and twisted Heegaard Floer homology
by Yi Ni

If a 3-manifold Y contains a nonseparating sphere, then some twisted
Heegaard Floer homology of Y is zero. This simple fact allows us to
prove several results about Dehn surgery on knots in such manifolds.
Similar results have been proved for knots in L-spaces.


(7) Cosimplicial models for the limit of the Goodwillie tower
by Rosona Eldred

We call attention to the intermediate constructions T_n F in
Goodwillie's Calculus of homotopy functors, giving a new model which
naturally gives rise to a family of towers filtering the Taylor tower
of a functor. We also establish a surprising equivalence between the
homotopy inverse limits of these towers and the homotopy inverse
limits of certain cosimplicial resolutions. This equivalence gives a
greatly simplified construction for the homotopy inverse limit of the
Taylor tower of a functor F under general assumptions.


(8) Homology of moduli spaces of linkages in high-dimensional Euclidean space
by Dirk Schutz

We study the topology of moduli spaces of closed linkages in R^d
depending on a length vector l in R^n. In particular, we use
equivariant Morse theory to obtain information on the homology groups
of these spaces, which works best for odd d. In the case d = 5 we
calculate the Poincare polynomial in terms of combinatorial
information encoded in the length vector.


(9) The Kunneth Theorem in equivariant K-theory
for actions of a cyclic group of order 2
by Jonathan Rosenberg

The Kuenneth Theorem for equivariant (complex) K-theory K^*_G, in the
form developed by Hodgkin and others, fails dramatically when G is a
finite group, and even when G is cyclic of order 2. We remedy this
situation in this very simplest case G=Z/2 by using the power of
RO(G)-graded equivariant K-theory.


(10) Parametrized ring-spectra and the nearby Lagrangian conjecture
by Thomas Kragh
Appendix: Mohammed Abouzaid

Let L be an embedded closed connected exact Lagrangian sub-manifold in
a connected cotangent bundle T*N. In this paper we prove that such an
embedding is, up to a finite covering space lift of T*N, a homology
equivalence. We prove this by constructing a fibrant parametrized
family of ring spectra FL parametrized by the manifold N. The homology
of FL will be (twisted) symplectic cohomology of T*L. The fibrancy
property will imply that there is a Serre spectral sequence converging
to the homology of FL. The fiber-wise ring structure combined with the
intersection product on N induces a product on this spectral
sequence. This product structure and its relation to the intersection
product on L is then used to obtain the result. Combining this result
with work of Abouzaid we arrive at the conclusion that L --> N is
always a homotopy equivalence.


(11) A universal characterization of higher algebraic K-theory
by Andrew Blumberg, David Gepner and Gonalo Tabuada

In this paper we establish a universal characterization of higher
algebraic K-theory in the setting of small stable infinity-categories.
Specifically, we prove that connective algebraic K-theory is the
universal additive invariant, ie the universal functor with values in
spectra which inverts Morita equivalences, preserves filtered
colimits, and satisfies Waldhausen's additivity theorem. Similarly,
we prove that nonconnective algebraic K-theory is the universal
localizing invariant, ie the universal functor that moreover satisfies
the Thomason-Trobaugh-Neeman Localization Theorem.

To prove these results, we construct and study two stable
infinity-categories of `noncommutative motives'; one associated to
additivity and another to localization. In these stable
infinity-categories, Waldhausen's S_dot-construction corresponds to
the suspension functor and connective and nonconnective algebraic
K-theory spectra become corepresentable by the noncommutative motive
of the sphere spectrum. In particular, the algebraic K-theory of every
scheme, stack, and ring spectrum can be recovered from these
categories of noncommutative motives. In the case of a connective ring
spectrum R, we prove moreover that its negative K-groups are
isomorphic to the negative K-groups of the ordinary ring pi_0(R).

In order to work with these categories of noncommutative motives, we
establish comparison theorems between the category of spectral
categories localized at the Morita equivalences and the category of
small idempotent-complete stable infinity-categories. We also explain
in detail the comparison between the infinity-categorical version of
Waldhausen K-theory and the classical definition.

As an application of our theory, we obtain a complete classification
of the natural transformations from higher algebraic K-theory to
topological Hochschild homology (THH) and topological cyclic
homology (TC). Notably, we obtain an elegant conceptual description
of the cyclotomic trace map.



Geometry & Topology Publications is an imprint of
Mathematical Sciences Publishers





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