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Nine papers published by Algebraic & Geometric Topology
Posted:
Jun 6, 2011 5:14 AM


Nine papers have been published by Algebraic & Geometric Topology
(1) Algebraic & Geometric Topology 11 (2011) 14971540 Surface links which are coverings over the standard torus by Inasa Nakamura URL: http://www.msp.warwick.ac.uk/agt/2011/1103/p050.xhtml DOI: 10.2140/agt.2011.11.1497
(2) Algebraic & Geometric Topology 11 (2011) 15411599 Homotopy theory of nonsymmetric operads by Fernando Muro URL: http://www.msp.warwick.ac.uk/agt/2011/1103/p051.xhtml DOI: 10.2140/agt.2011.11.1541
(3) Algebraic & Geometric Topology 11 (2011) 16011648 4fold symmetric quandle invariants of 3manifolds by Takefumi Nosaka URL: http://www.msp.warwick.ac.uk/agt/2011/1103/p052.xhtml DOI: 10.2140/agt.2011.11.1601
(4) Algebraic & Geometric Topology 11 (2011) 16491699 Pinwheels and nullhomologous surgery on 4manifolds with b^+=1 by Ronald Fintushel and Ronald J Stern URL: http://www.msp.warwick.ac.uk/agt/2011/1103/p053.xhtml DOI: 10.2140/agt.2011.11.1649
(5) Algebraic & Geometric Topology 11 (2011) 17011707 C^1actions of BaumslagSolitar groups on S^1 by Nancy Guelman and Isabelle Liousse URL: http://www.msp.warwick.ac.uk/agt/2011/1103/p054.xhtml DOI: 10.2140/agt.2011.11.1701
(6) Algebraic & Geometric Topology 11 (2011) 17091735 On R,L~Cohen's zetaelement by Xiugui Liu URL: http://www.msp.warwick.ac.uk/agt/2011/1103/p055.xhtml DOI: 10.2140/agt.2011.11.1709
(7) Algebraic & Geometric Topology 11 (2011) 17371766 Obtaining presentations from group actions without making choices by Andrew Putman URL: http://www.msp.warwick.ac.uk/agt/2011/1103/p056.xhtml DOI: 10.2140/agt.2011.11.1737
(8) Algebraic & Geometric Topology 11 (2011) 17671780 A new action of the KudoArakiMay 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/2011/1103/p057.xhtml DOI: 10.2140/agt.2011.11.1767
(9) Algebraic & Geometric Topology 11 (2011) 17811792 Multiple genus 2 Heegaard splittings: a missed case by John Berge and Martin Scharlemann URL: http://www.msp.warwick.ac.uk/agt/2011/1103/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 4space. We construct a surface link as a branched covering over the standard torus, which we call a toruscovering link. We show that a certain toruscovering T^2link is equivalent to the split union of spun T^2links and turned spun T^2links. We show that a certain toruscovering T^2link has a nonclassical link group. We give a certain class of ribbon toruscovering T^2links. We present the quandle cocycle invariant of a certain toruscovering T^2link 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) 4fold symmetric quandle invariants of 3manifolds by Takefumi Nosaka
The paper introduces 4fold symmetric quandles and 4fold symmetric quandle homotopy invariants of 3manifolds. We classify 4fold 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 4fold symmetric quandle homotopy invariant. We also discuss symmetric quandle cocycle invariants and coloring polynomials of 4fold symmetric quandles.
(4) Pinwheels and nullhomologous surgery on 4manifolds with b^+=1 by Ronald Fintushel and Ronald J Stern
We present a method for finding embedded nullhomologous tori in standard 4manifolds which can be utilized to change their smooth structure. As an application, we show how to obtain infinite families of simply connected smooth 4manifolds with b^+=1 and b^=2,...,7, via surgery on nullhomologous tori embedded in the standard manifolds CP^2 # k CP^2bar, k=2,...,7.
(5) C^1actions of BaumslagSolitar groups on S^1 by Nancy Guelman and Isabelle Liousse
Let BS(1,n) = < a, b  aba^{1} = b^n > be the solvable BaumslagSolitar 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 zetaelement by Xiugui Liu
Let p be a prime greater than three. In the plocal stable homotopy groups of spheres, R L Cohen constructed the infinite zetaelement zeta_{n1}in pi_{2p^{n+1}2p^n+2p5}(S) of order p. In the stable homotopy group pi_{2p^{n+1}2p^n+2p^23}(V(1)) of the SmithToda 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^22s2p} denote the SpanierWhitehead dual of the generator beta''_s =beta^s i_1 i_0 in pi_{2sp^22s}(V(1)), which defines the betaelement beta_s. Let xi_{s,k}=beta_{s1}^{ast}varpi_k. In this paper, we show that the composite of R L Cohen's zetaelement zeta_{n1} with xi_{s,n} is nontrivial, where n>4 and 1<s<p1. As a corollary, xi_{s,n} is also nontrivial for 1 < s < p1.
(7) Obtaining presentations from group actions without making choices by Andrew Putman
Consider a group G acting nicely on a simplyconnected 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 2connected, 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 KudoArakiMay 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 Agenerators 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 KudoArakiMay algebra K, and consider the Kmodule structure of the primitives, which form a sub Kalgebra of the dual of the infinite symmetric algebra. Our examples show that the Kaction 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 3manifolds", in "Proceedings of the Kirbyfest", Geom. Topol. Monogr. 2 (1999) 489553] is explored: new examples are found of closed orientable 3manifolds 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.
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