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Obtaining genus 2 Heegaard splittings from Dehn surgery
genus 2 Heegaard splittings Dehn surgery Geometric Topology
2012/5/9
Let K' be a hyperbolic knot in S^3 and suppose that some Dehn surgery on K' with distance at least 3 from the meridian yields a 3-manifold M of Heegaard genus 2. We show that if M does not contain an ...
Central cohomology operations and K-theory
K-theory operations cobordism Algebraic Topology
2012/4/16
For stable degree zero operations, and also for additive unstable operations of bidegree (0,0), it is known that the centre of the ring of operations for complex cobordism is isomorphic to the corresp...
We study the bilipschitz equivalence type of tree-graded spaces, showing that asymptotic cones of relatively hyperbolic groups (resp. asymptotic cones of groups containing a cut-point) only depend on ...
The Poincare-Hopf Theorem for relative braid classes
Poincare-Hopf Theorem relative braid classes Symplectic Geometry
2012/4/18
Braid Floer homology is an invariant of proper relative braid classes. Closed integral curves of 1-periodic Hamiltonian vector fields on the 2-disc may be regarded as braids. If the Braid Floer homolo...
Arc index of pretzel knots of type $(-p,q,r)$
knot pretzel knot arc presentation arc index Kauffman polynomial
2012/4/18
We computed the arc index for the pretzel knots $K=P(-p,q,r)$ with $p,q,r\ge2$, $r\geq q$ and at most one of $p,q,r$ is even. If $q=2$, then the arc index $\alpha(K)$ equals the minimal crossing numbe...
Logarithmic structures on K-theory spectra
Symmetric spectra log structures E-infinity spaces group completion topological Andre-Quillen homology
2012/4/23
We study a modified version of Rognes' logarithmic structures on structured ring spectra. In our setup, we obtain canonical logarithmic structures on connective K-theory spectra which approximate the ...
The Complex of Non-separating embedded spheres
Complex of Non-separating embedded spheres Geometric Topology
2012/4/17
For n >2, we shall show that the group Aut(NS(M)) of simplicial automorphisms of the complex NS(M) of non-separating embedded spheres in the manifold M,connected sum of n copies of S^2 X S^1, isomorph...
The Ghost length, levels and shriek maps on classifying spaces
Level ghost length Gorenstein space shriek map
2012/4/17
We give a lower bound of the cochain type level of the diagonal map on the classifying space of a Lie group by using the ghostness of a shriek map. Moreover, in a derived category, we discuss the triv...
We show that the Kakimizu complex of minimal genus Seifert surfaces for a knot in the 3-sphere is quasi-isometric to a Euclidean integer lattice $\mathbb Z^n$ for some $n \geq 0$.
Context-free manifold calculus and the Fulton-MacPherson Operad
Embedding calculus Fulton-MacPherson operad Algebraic Topology
2012/4/18
The paper gives an explicit description of the Weiss embedding tower in terms of spaces of maps of truncated modules over the framed Fulton-MacPherson operad.
Combinatorial realisation of cycles and small covers
Combinatorial realisation cycles small covers Algebraic Topology
2012/4/17
In 1940s Steenrod asked if every homology class $z\in H_n(X,\mathbb{Z})$ of every topological space $X$ can be realised by an image of the fundamental class of an oriented closed smooth manifold. Thom...
HF=HM V: Seiberg-Witten-Floer homology and handle addition
Seiberg-Witten-Floer homology handle addition Geometric Topology
2012/4/17
This is the last of five papers that construct an isomorphism between the Seiberg-Witten Floer homology and the Heegaard Floer homology of a given compact, oriented 3-manifold.
On the existence of stable compact leaves for transversely holomorphic foliations
Holomorphic foliation holonomy stable leaf
2012/4/17
A transversely holomorphic foliation on a compact complex manifold, exhibits a compact stable leaf if and only if the set of compact leaves is not a zero measure subset of the manifold.
On uniform metrizability of the functor of idempotent probability measures
uniformly metrizability of functors idempotent probability measures General Topology
2012/4/17
In the present paper we show that the functor of idempotent probability measures satisfies all of conditions with an additional claim of uniform metrizability of functors.
Skein algebras and cluster algebras of marked surfaces
Skein algebras cluster algebras marked surfaces Quantum Algebra Geometric Topology
2012/4/17
This paper defines several algebras associated to an oriented surface S with a finite set of marked points on the boundary. The first is the skein algebra Sk_q(S), which is spanned by links in the sur...