Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.
|
|
|
|
Eleven papers published by GTP completing 2011 publication
Posted:
Dec 26, 2011 11:30 AM
|
|
This announcement completes GTP publication for 2011.
Papers (1)-(5) complete AGT Volume 11 (2011) and papers (6)-(11)
complete GT Volume 15 (2011). Publiction in 2012 will commence on
January 1 2012. Seasons greetings to all!
Five papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 11 (2011) 2941-2970
Representation spaces of pretzel knots
by Raphael Zentner
URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p095.xhtml
DOI: 10.2140/agt.2011.11.2941
(2) Algebraic & Geometric Topology 11 (2011) 2971-3010
Reducible braids and Garside Theory
by Juan Gonzalez-Meneses and Bert Wiest
URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p096.xhtml
DOI: 10.2140/agt.2011.11.2971
(3) Algebraic & Geometric Topology 11 (2011) 3011-3041
Representation stability for the cohomology of the moduli space M_g^n
by Rita Jimenez Rolland
URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p097.xhtml
DOI: 10.2140/agt.2011.11.3011
(4) Algebraic & Geometric Topology 11 (2011) 3043-3064
The Fox property for codimension one embeddings of products of three spheres into spheres
by Laercio Aparecido Lucas and Osamu Saeki
URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p098.xhtml
DOI: 10.2140/agt.2011.11.3043
(5) Algebraic & Geometric Topology 11 (2011) 3065-3084
Constructing free actions of p-groups on products of spheres
by Michele Klaus
URL: http://www.msp.warwick.ac.uk/agt/2011/11-05/p099.xhtml
DOI: 10.2140/agt.2011.11.3065
Six papers have been published by Geometry & Topology
(6) Geometry & Topology 15 (2011) 2181-2233
Strongly contracting geodesics in Outer Space
by Yael Algom-Kfir
URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p054.xhtml
DOI: 10.2140/gt.2011.15.2181
(7) Geometry & Topology 15 (2011) 2235-2273
Rigidity of spherical codes
by Henry Cohn, Yang Jiao, Abhinav Kumar and Salvatore Torquato
URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p055.xhtml
DOI: 10.2140/gt.2011.15.2235
(8) Geometry & Topology 15 (2011) 2275-2298
On intrinsic geometry of surfaces in normed spaces
by Dmitri Burago and Sergei Ivanov
URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p056.xhtml
DOI: 10.2140/gt.2011.15.2275
(9) Geometry & Topology 15 (2011) 2299-2319
Rigidity of polyhedral surfaces, III
by Feng Luo
URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p057.xhtml
DOI: 10.2140/gt.2011.15.2299
(10) Geometry & Topology 15 (2011) 2321-2350
Counting lattice points in compactified moduli spaces of curves
by Norman Do and Paul Norbury
URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p058.xhtml
DOI: 10.2140/gt.2011.15.2321
(11) Geometry & Topology 15 (2011) 2351-2457
Intersection theory of punctured pseudoholomorphic curves
by Richard Siefring
URL: http://www.msp.warwick.ac.uk/gt/2011/15-04/p059.xhtml
DOI: 10.2140/gt.2011.15.2351
Abstracts follow
(1) Representation spaces of pretzel knots
by Raphael Zentner
We study the representation spaces R(K;i) appearing in Kronheimer and
Mrowka's instanton knot Floer homologies for a class of pretzel
knots. In particular, for pretzel knots P(p,q,r) with p, q, r pairwise
coprime, these appear to be nondegenerate and comprise representations
in SU(2) that are not binary dihedral.
(2) Reducible braids and Garside Theory
by Juan Gonzalez-Meneses and Bert Wiest
We show that reducible braids which are, in a Garside-theoretical
sense, as simple as possible within their conjugacy class, are also as
simple as possible in a geometric sense. More precisely, if a braid
belongs to a certain subset of its conjugacy class which we call the
stabilized set of sliding circuits, and if it is reducible, then its
reducibility is geometrically obvious: it has a round or almost round
reducing curve. Moreover, for any given braid, an element of its
stabilized set of sliding circuits can be found using the well-known
cyclic sliding operation. This leads to a polynomial time algorithm
for deciding the Nielsen-Thurston type of any braid, modulo one
well-known conjecture on the speed of convergence of the cyclic
sliding operation.
(3) Representation stability for the cohomology of the moduli space M_g^n
by Rita Jimenez Rolland
Let M_g^n be the moduli space of Riemann surfaces of genus g with n
labeled marked points. We prove that, for g >= 2, the cohomology
groups {H^i(M_g^n;Q)}_{n=1}^{\infty} form a sequence of
S_n-representations which is representation stable in the sense of
Church-Farb. In particular this result applied to the trivial
S_n-representation implies rational "puncture homological stability"
for the mapping class group Mod_g^n. We obtain representation
stability for sequences {H^i(PMod^n(M);Q)}_{n=1}^{\infty}, where
PMod^n(M) is the mapping class group of many connected orientable
manifolds M of dimension d >= 3 with centerless fundamental group; and
for sequences {H^i(BPDiff^n(M);Q)}_{n=1}^{\infty}, where BPDiff^n(M)
is the classifying space of the subgroup PDiff^n(M) of diffeomorphisms
of M that fix pointwise n distinguished points in M.
(4) The Fox property for codimension one embeddings of products of three spheres into spheres
by Laercio Aparecido Lucas and Osamu Saeki
Fox has shown that for every closed connected surface smoothly
embedded in S^3, the closure of each component of its complement is
diffeomorphic to the closure of the complement of a handlebody
embedded in S^3. In this paper, we study a similar `Fox property'
for smooth embeddings of S^p x S^q x S^r in S^{p+q+r+1}.
(5) Constructing free actions of p-groups on products of spheres
by Michele Klaus
We prove that, for p an odd prime, every finite p-group of rank 3 acts
freely on a finite complex X homotopy equivalent to a product of three
spheres.
(6) Strongly contracting geodesics in Outer Space
by Yael Algom-Kfir
We study the Lipschitz metric on Outer Space and prove that fully
irreducible elements of Out(F_n) act by hyperbolic isometries with axes
which are strongly contracting. As a corollary, we prove that the axes of
fully irreducible automorphisms in the Cayley graph of Out(F_n) are Morse,
meaning that a quasi-geodesic with endpoints on the axis stays within
a bounded distance from the axis.
(7) Rigidity of spherical codes
by Henry Cohn, Yang Jiao, Abhinav Kumar and Salvatore Torquato
A packing of spherical caps on the surface of a sphere (that is, a
spherical code) is called rigid or jammed if it is isolated within the
space of packings. In other words, aside from applying a global isometry,
the packing cannot be deformed. In this paper, we systematically study
the rigidity of spherical codes, particularly kissing configurations.
One surprise is that the kissing configuration of the Coxeter-Todd
lattice is not jammed, despite being locally jammed (each individual
cap is held in place if its neighbors are fixed); in this respect, the
Coxeter-Todd lattice is analogous to the face-centered cubic lattice in
three dimensions. By contrast, we find that many other packings have
jammed kissing configurations, including the Barnes-Wall lattice and
all of the best kissing configurations known in four through twelve
dimensions. Jamming seems to become much less common for large kissing
configurations in higher dimensions, and in particular it fails for
the best kissing configurations known in 25 through 31 dimensions.
Motivated by this phenomenon, we find new kissing configurations in
these dimensions, which improve on the records set in 1982 by the
laminated lattices.
(8) On intrinsic geometry of surfaces in normed spaces
by Dmitri Burago and Sergei Ivanov
We prove three facts about intrinsic geometry of surfaces in a normed
(Minkowski) space. When put together, these facts demonstrate a rather
intriguing picture. We show that (1) geodesics on saddle surfaces (in
a space of any dimension) behave as they are expected to: they have no
conjugate points and thus minimize length in their homotopy class; (2)
in contrast, every two-dimensional Finsler manifold can be locally
embedded as a saddle surface in a 4-dimensional space; and (3)
geodesics on convex surfaces in a 3-dimensional space also behave as
they are expected to: on a complete strictly convex surface, no
complete geodesic minimizes the length globally.
(9) Rigidity of polyhedral surfaces, III
by Feng Luo
This paper investigates several global rigidity issues for polyhedral
surfaces including inversive distance circle packings. Inversive
distance circle packings are polyhedral surfaces introduced by P
Bowers and K Stephenson in [Mem. Amer. Math. Soc. 170, no. 805,
Amer. Math. Soc. (2004)] as a generalization of Andreev and
Thurston's circle packing. They conjectured that inversive distance
circle packings are rigid. We prove this conjecture using recent work
of R Guo [Trans. Amer. Math. Soc. 363 (2011) 4757--4776] on the
variational principle associated to the inversive distance circle
packing. We also show that each polyhedral metric on a triangulated
surface is determined by various discrete curvatures that we
introduced in [arXiv 0612.5714], verifying a conjecture in [arXiv
0612.5714]. As a consequence, we show that the discrete Laplacian
operator determines a spherical polyhedral metric.
(10) Counting lattice points in compactified moduli spaces of curves
by Norman Do and Paul Norbury
We define and count lattice points in the moduli space bar{M}_{g,n}
of stable genus g curves with n labeled points. This extends a
construction of the second author for the uncompactified moduli space
M_{g,n}. The enumeration produces polynomials whose top degree
coefficients are tautological intersection numbers on bar{M}_{g,n}
and whose constant term is the orbifold Euler characteristic of
bar{M}_{g,n}. We prove a recursive formula which can be used to
effectively calculate these polynomials. One consequence of these
results is a simple recursion relation for the orbifold Euler
characteristic of bar{M}_{g,n}.
(11) Intersection theory of punctured pseudoholomorphic curves
by Richard Siefring
We study the intersection theory of punctured pseudoholomorphic curves
in 4-dimensional symplectic cobordisms. Using the asymptotic results
of the author [Comm. Pure Appl. Math. 61(2008) 1631--84], we first
study the local intersection properties of such curves at the
punctures. We then use this to develop topological controls on the
intersection number of two curves. We also prove an adjunction
formula which gives a topological condition that will guarantee a
curve in a given homotopy class is embedded, extending previous work
of Hutchings [JEMS 4(2002) 313--61].
We then turn our attention to curves in the symplectization R x M of a
3-manifold M admitting a stable Hamiltonian structure. We investigate
controls on intersections of the projections of curves to the
3-manifold and we present conditions that will guarantee the
projection of a curve to the 3-manifold is an embedding.
Finally we consider an application concerning pseudoholomorphic curves
in manifolds admitting a certain class of holomorphic open book
decomposition and an application concerning the existence of
generalized pseudoholomorphic curves, as introduced by Hofer
[Geom. Func. Anal. (2000) 674--704] .
Geometry & Topology Publications is an imprint of
Mathematical Sciences Publishers
|
|
|
|
