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Nine papers published by Algebraic & Geometric Topology
Posted:
Jun 6, 2011 5:14 AM
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Nine papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 11 (2011) 1497-1540
Surface links which are coverings over the standard torus
by Inasa Nakamura
URL: http://www.msp.warwick.ac.uk/agt/2011/11-03/p050.xhtml
DOI: 10.2140/agt.2011.11.1497
(2) Algebraic & Geometric Topology 11 (2011) 1541-1599
Homotopy theory of nonsymmetric operads
by Fernando Muro
URL: http://www.msp.warwick.ac.uk/agt/2011/11-03/p051.xhtml
DOI: 10.2140/agt.2011.11.1541
(3) Algebraic & Geometric Topology 11 (2011) 1601-1648
4-fold symmetric quandle invariants of 3-manifolds
by Takefumi Nosaka
URL: http://www.msp.warwick.ac.uk/agt/2011/11-03/p052.xhtml
DOI: 10.2140/agt.2011.11.1601
(4) Algebraic & Geometric Topology 11 (2011) 1649-1699
Pinwheels and nullhomologous surgery on 4-manifolds with b^+=1
by Ronald Fintushel and Ronald J Stern
URL: http://www.msp.warwick.ac.uk/agt/2011/11-03/p053.xhtml
DOI: 10.2140/agt.2011.11.1649
(5) Algebraic & Geometric Topology 11 (2011) 1701-1707
C^1-actions of Baumslag-Solitar groups on S^1
by Nancy Guelman and Isabelle Liousse
URL: http://www.msp.warwick.ac.uk/agt/2011/11-03/p054.xhtml
DOI: 10.2140/agt.2011.11.1701
(6) Algebraic & Geometric Topology 11 (2011) 1709-1735
On R,L~Cohen's zeta-element
by Xiugui Liu
URL: http://www.msp.warwick.ac.uk/agt/2011/11-03/p055.xhtml
DOI: 10.2140/agt.2011.11.1709
(7) Algebraic & Geometric Topology 11 (2011) 1737-1766
Obtaining presentations from group actions without making choices
by Andrew Putman
URL: http://www.msp.warwick.ac.uk/agt/2011/11-03/p056.xhtml
DOI: 10.2140/agt.2011.11.1737
(8) Algebraic & Geometric Topology 11 (2011) 1767-1780
A new action of the Kudo-Araki-May algebra on the dual of the
symmetric algebras, with applications to the hit problem
by David Pengelley and Frank Williams
URL: http://www.msp.warwick.ac.uk/agt/2011/11-03/p057.xhtml
DOI: 10.2140/agt.2011.11.1767
(9) Algebraic & Geometric Topology 11 (2011) 1781-1792
Multiple genus 2 Heegaard splittings: a missed case
by John Berge and Martin Scharlemann
URL: http://www.msp.warwick.ac.uk/agt/2011/11-03/p058.xhtml
DOI: 10.2140/agt.2011.11.1781
Abstracts follow
(1) Surface links which are coverings over the standard torus
by Inasa Nakamura
We introduce a new construction of a surface link in 4-space. We
construct a surface link as a branched covering over the standard
torus, which we call a torus-covering link. We show that a certain
torus-covering T^2-link is equivalent to the split union of spun
T^2-links and turned spun T^2-links. We show that a certain
torus-covering T^2-link has a nonclassical link group. We give a
certain class of ribbon torus-covering T^2-links. We present the
quandle cocycle invariant of a certain torus-covering T^2-link
obtained from a classical braid, by using the quandle cocycle
invariants of the closure of the braid.
(2) Homotopy theory of nonsymmetric operads
by Fernando Muro
We endow categories of nonsymmetric operads with natural model
structures. We work with no restriction on our operads and only assume
the usual hypotheses for model categories with a symmetric monoidal
structure. We also study categories of algebras over these operads in
enriched nonsymmetric monoidal model categories.
(3) 4-fold symmetric quandle invariants of 3-manifolds
by Takefumi Nosaka
The paper introduces 4-fold symmetric quandles and 4-fold symmetric
quandle homotopy invariants of 3-manifolds. We classify 4-fold
symmetric quandles and investigate their properties. When the quandle
is finite, we explicitly determine a presentation of its inner
automorphism group. We calculate the container of the 4-fold
symmetric quandle homotopy invariant. We also discuss symmetric
quandle cocycle invariants and coloring polynomials of 4-fold
symmetric quandles.
(4) Pinwheels and nullhomologous surgery on 4-manifolds with b^+=1
by Ronald Fintushel and Ronald J Stern
We present a method for finding embedded nullhomologous tori in
standard 4-manifolds which can be utilized to change their smooth
structure. As an application, we show how to obtain infinite families
of simply connected smooth 4-manifolds with b^+=1 and b^-=2,...,7, via
surgery on nullhomologous tori embedded in the standard manifolds CP^2
# k CP^2-bar, k=2,...,7.
(5) C^1-actions of Baumslag-Solitar groups on S^1
by Nancy Guelman and Isabelle Liousse
Let BS(1,n) = < a, b | aba^{-1} = b^n > be the solvable
Baumslag--Solitar group, where n is at least 2. It is known that
BS(1,n) is isomorphic to the group generated by the two affine maps of
the line: f_0(x) = x + 1 and h_0(x) = nx. The action on the circle
which is the real line union the point at infinity generated by these
two affine maps f_0 and h_0 is called the standard affine one. We
prove that any faithful representation of BS(1,n) into the group of
C^1 diffeomorphisms of the circle is semiconjugated (up to a finite
index subgroup) to the standard affine action.
(6) On R,L~Cohen's zeta-element
by Xiugui Liu
Let p be a prime greater than three. In the p-local stable
homotopy groups of spheres, R L Cohen constructed the infinite
zeta-element zeta_{n-1}in pi_{2p^{n+1}-2p^n+2p-5}(S) of
order p. In the stable homotopy group
pi_{2p^{n+1}-2p^n+2p^2-3}(V(1)) of the Smith--Toda spectrum V(1),
X Liu constructed an essential element varpi_k for k at least 3.
Let beta_s^{ast}= j_0 j_1 beta^s in [V(1),S]_{2sp^2-2s-2p}
denote the Spanier--Whitehead dual of the generator
beta''_s =beta^s i_1 i_0 in pi_{2sp^2-2s}(V(1)),
which defines the beta-element beta_s. Let
xi_{s,k}=beta_{s-1}^{ast}varpi_k. In this paper, we show that
the composite of R L Cohen's zeta-element zeta_{n-1} with
xi_{s,n} is nontrivial, where n>4 and 1<s<p-1. As a
corollary, xi_{s,n} is also nontrivial for 1 < s < p-1.
(7) Obtaining presentations from group actions without making choices
by Andrew Putman
Consider a group G acting nicely on a simply-connected
simplicial complex X. Numerous classical methods exist
for using this group action to produce a presentation for G. For
the case that X/G is 2-connected, we give a new method that
has the novelty that one does not have to identify a fundamental domain
for the action. Indeed, the resulting presentation is canonical in
the sense that no arbitrary choices need to be made. It can be viewed
as a nonabelian analogue of a simple result in the study of equivariant
homology.
(8) A new action of the Kudo-Araki-May algebra on the dual of the
symmetric algebras, with applications to the hit problem
by David Pengelley and Frank Williams
The hit problem for a cohomology module over the Steenrod algebra A
asks for a minimal set of A-generators for the module. In this paper we
consider the symmetric algebras over the field F_p, for p an arbitrary
prime, and treat the equivalent problem of determining the set of
A^*-primitive elements in their duals. We produce a method for generating
new primitives from known ones via a new action of the Kudo-Araki-May
algebra K, and consider the K-module structure of the primitives, which
form a sub K-algebra of the dual of the infinite symmetric algebra. Our
examples show that the K-action on the primitives is not free. Our new
action encompasses, on the finite symmetric algebras, the operators
introduced by Kameko for studying the hit problem.
(9) Multiple genus 2 Heegaard splittings: a missed case
by John Berge and Martin Scharlemann
A gap in [H Rubinstein and M Scharlemann, "Genus two Heegaard splittings
of orientable 3-manifolds", in "Proceedings of the Kirbyfest", Geom.
Topol. Monogr. 2 (1999) 489-553] is explored: new examples are found of
closed orientable 3-manifolds with possibly multiple genus 2 Heegaard
splittings. Properties common to all the examples in that paper are
not universally shared by the new examples: some of the new examples
have Hempel distance 3, and it is not clear that a single stabilization
always makes the multiple splittings isotopic.
Geometry & Topology Publications is an imprint of
Mathematical Sciences Publishers
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