Nine papers published by Geometry & Topology Publications
Geometry and Topology
papers (7)-(9) complete issue 1 of GT Volume 14.
Six papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 10 (2010) 87-136
Bar constructions and Quillen homology of modules over operads
by John E Harper
URL: http://www.msp.warwick.ac.uk/agt/2010/10-01/p004.xhtml
DOI: 10.2140/agt.2010.10.87
(2) Algebraic & Geometric Topology 10 (2010) 137-213
Generalized spectral categories, topological
Hochschild homology and trace maps
by Goncalo Tabuada
URL: http://www.msp.warwick.ac.uk/agt/2010/10-01/p005.xhtml
DOI: 10.2140/agt.2010.10.137
(3) Algebraic & Geometric Topology 10 (2010) 215-217
Quasimorphisms and laws
by Danny Calegari
URL: http://www.msp.warwick.ac.uk/agt/2010/10-01/p006.xhtml
DOI: 10.2140/agt.2010.10.215
(4) Algebraic & Geometric Topology 10 (2010) 219-274
Nerves and classifying spaces for bicategories
by Pilar Carrasco, Antonio M Cegarra and Antonio R Garzon
URL: http://www.msp.warwick.ac.uk/agt/2010/10-01/p007.xhtml
DOI: 10.2140/agt.2010.10.219
(5) Algebraic & Geometric Topology 10 (2010) 275-292
On Hopkins' Picard group Pic_2 at the prime 3
by Nasko Karamanov
URL: http://www.msp.warwick.ac.uk/agt/2010/10-01/p008.xhtml
DOI: 10.2140/agt.2010.10.275
(6) Algebraic & Geometric Topology 10 (2010) 293-314
A family of transversely nonsimple knots
by Tirasan Khandhawit and Lenhard Ng
URL: http://www.msp.warwick.ac.uk/agt/2010/10-01/p009.xhtml
DOI: 10.2140/agt.2010.10.293
Three papers have been published by Geometry & Topology
(7) Geometry & Topology 14 (2010) 573-584
A finitely generated, locally indicable group with no
faithful action by C^1 diffeomorphisms of the interval
by Andres Navas
URL: http://www.msp.warwick.ac.uk/gt/2010/14-01/p012.xhtml
DOI: 10.2140/gt.2010.14.573
(8) Geometry & Topology 14 (2010) 585-609
Topological Index Theory for surfaces in 3-manifolds
by David Bachman
URL: http://www.msp.warwick.ac.uk/gt/2010/14-01/p013.xhtml
DOI: 10.2140/gt.2010.14.585
(9) Geometry & Topology 14 (2010) 611-626
Non-negative Legendrian isotopy in ST^*M
by Vladimir Chernov and Stefan Nemirovski
URL: http://www.msp.warwick.ac.uk/gt/2010/14-01/p014.xhtml
DOI: 10.2140/gt.2010.14.611
Abstracts follow
(1) Bar constructions and Quillen homology of modules over operads
by John E Harper
We show that topological Quillen homology of algebras and modules over
operads in symmetric spectra can be calculated by realizations of
simplicial bar constructions. Working with several model category
structures, we give a homotopical proof after showing that certain
homotopy colimits in algebras and modules over operads can be easily
understood. A key result here, which lies at the heart of this paper,
is showing that the forgetful functor commutes with certain homotopy
colimits. We also prove analogous results for algebras and modules
over operads in unbounded chain complexes.
(2) Generalized spectral categories, topological
Hochschild homology and trace maps
by Goncalo Tabuada
Given a monoidal model category C and an object K in C, Hovey
constructed the monoidal model category Sp^Sigma(C,K) of K-symmetric
spectra over C. In this paper we describe how to lift a model
structure on the category of C-enriched categories to the category of
Sp^Sigma(C,K)-enriched categories. This allow us to construct a (four
step) zig-zag of Quillen equivalences comparing dg categories to
HZ-categories. As an application we obtain: (1) the invariance under
weak equivalences of the topological Hochschild homology (THH) and
topological cyclic homology (TC) of dg categories; (2) non-trivial
natural transformations from algebraic K-theory to THH.
(3) Quasimorphisms and laws
by Danny Calegari
Stable commutator length vanishes in any group that obeys a law.
(4) Nerves and classifying spaces for bicategories
by Pilar Carrasco, Antonio M Cegarra and Antonio R Garzon
This paper explores the relationship amongst the various simplicial
and pseudosimplicial objects characteristically associated to any
bicategory C. It proves the fact that the geometric realizations of
all of these possible candidate "nerves of C" are homotopy
equivalent. Any one of these realizations could therefore be taken as
_the_ classifying space BC of the bicategory. Its other major result
proves a direct extension of Thomason's "Homotopy Colimit Theorem" to
bicategories: When the homotopy colimit construction is carried out on
a diagram of spaces obtained by applying the classifying space functor
to a diagram of bicategories, the resulting space has the homotopy
type of a certain bicategory, called the "Grothendieck construction on
the diagram". Our results provide coherence for all reasonable
extensions to bicategories of Quillen's definition of the "classifying
space" of a category as the geometric realization of the category's
Grothendieck nerve, and they are applied to monoidal (tensor)
categories through the elemental "delooping" construction.
(5) On Hopkins' Picard group Pic_2 at the prime 3
by Nasko Karamanov
In this paper we calculate the algebraic Hopkins Picard group
Pic_2^{alg} at the prime p=3, which is a subgroup of the group of
isomorphism classes of invertible K(2)-local spectra, ie of Hopkins'
Picard group Pic_2. We use the resolution of the K(2)-local sphere
introduced by Goerss, Henn, Mahowald and Rezk in [Ann. of Math (2) 162
(2005) 777-822] and the methods from Henn, Karamanov and Mahowald [to
appear in Math. Zeit. arXiv:0811.0235] and Karamanov [PhD thesis,
Universite Louis Pasteur (2006)].
(6) A family of transversely nonsimple knots
by Tirasan Khandhawit and Lenhard Ng
We apply knot Floer homology to exhibit an infinite family of
transversely nonsimple prime knots starting with 10_{132}. We also
discuss the combinatorial relationship between grid diagrams, braids
and Legendrian and transverse knots in standard contact R^3.
(7) A finitely generated, locally indicable group with no
faithful action by C^1 diffeomorphisms of the interval
by Andres Navas
According to Thurston's stability theorem, every group of C^1
diffeomorphisms of the closed interval is locally indicable (that is,
every finitely generated subgroup factors through Z). We show that,
even for finitely generated groups, the converse of this statement is
not true. More precisely, we show that the group F_2 wreath Z^2,
although locally indicable, does not embed into Diff_+^1(]0,1[).
(Here F_2 is any free subgroup of SL(2,Z), and its action on Z^2 is
the linear one.) Moreover, we show that for every non-solvable
subgroup G of SL(2,Z), the group G wreath Z^2 does not embed into
Diff^1_+(S^1).
(8) Topological Index Theory for surfaces in 3-manifolds
by David Bachman
The disk complex of a surface in a 3--manifold is used to define its
topological index. Surfaces with well-defined topological index are
shown to generalize well known classes, such as incompressible,
strongly irreducible and critical surfaces. The main result is that
one may always isotope a surface H with topological index n to meet an
incompressible surface F so that the sum of the indices of the
components of H \ N(F) is at most n. This theorem and its corollaries
generalize many known results about surfaces in 3--manifolds, and
often provides more efficient proofs. The paper concludes with a list
of questions and conjectures, including a natural generalization of
Hempel's distance to surfaces with topological index >=2.
(9) Non-negative Legendrian isotopy in ST^*M
by Vladimir Chernov and Stefan Nemirovski
It is shown that if the universal cover of a manifold M is an open
manifold, then two different fibres of the spherical cotangent bundle
ST^*M cannot be connected by a non-negative Legendrian isotopy. This
result is applied to the study of causality in globally hyperbolic
spacetimes. It is also used to strengthen a result of Eliashberg, Kim
and Polterovich on the existence of a partial order on Cont_0(ST^*M).
surajit debarati
wrote:
Sir,
I wrote 2 papers on Euclidian geomety. Its about proof of 2
theorems which simplify the Euclidian Geometry. I am an undergraduate
student of Computer Sc Engineering. How & where i shall publish those
papers,if you kindly inform me.
from,
Surajit Dutta.