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Mathematische Annalen : Volume 367, Issue 3-4, April 2017

Nonexistence of solutions to parabolic differential inequalities with a potential on Riemannian manifolds

Algebraic isomonodromic deformations of logarithmic connections on the Riemann sphere and finite braid group orbits on character varieties

Volume gradients and homology in towers of residually-free groups

Finite type annular ends for harmonic functions

On probability measures arising from lattice points on circles

Affine and linear invariant families of harmonic mappings

The arithmetic Hodge index theorem for adelic line bundles

Eisenstein series on rank 2 hyperbolic Kac–Moody groups

Maximal amenable subalgebras of von Neumann algebras associated with hyperbolic groups

The tropical momentum map: a classification of toric log symplectic manifolds

On irreducible subgroups of simple algebraic groups

Algebraic (volume) density property for affine homogeneous spaces

Small Lefschetz fibrations and exotic 4-manifolds

Global radial solutions to 3D relativistic Euler equations for non-isentropic Chaplygin gases

Local systems on the free loop space and finiteness of the Hofer-Zehnder capacity

Balanced metrics on twisted Higgs bundles

On short time existence of Lagrangian mean curvature flow

Finite type invariants of w-knotted objects II: tangles, foams and the Kashiwara–Vergne problem

Une interprétation modulaire de la variété trianguline

The adiabatic limit of Schrödinger operators on fibre bundles

ALE scalar-flat Kähler metrics on non-compact weighted projective spaces

Generalized semi-invariant distributions on p-adic spaces

Shellable weakly compact subsets of C[0, 1]

2-Cycles on higher Fano hypersurfaces

Stable maps and branched shadows of 3-manifolds

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Finite type invariants of w-knotted objects II: tangles, foams and the Kashiwara–Vergne problem

Content Provider	Springer Nature Link
Author	Bar Natan, Dror Dancso, Zsuzsanna
Copyright Year	2016
Abstract	This is the second in a series of papers dedicated to studying w-knots, and more generally, w-knotted objects (w-braids, w-tangles, etc.). These are classes of knotted objects that are wider but weaker than their “usual” counterparts. To get (say) w-knots from usual knots (or u-knots), one has to allow non-planar “virtual” knot diagrams, hence enlarging the base set of knots. But then one imposes a new relation beyond the ordinary collection of Reidemeister moves, called the “overcrossings commute” relation, making w-knotted objects a bit weaker once again. Satoh (J. Knot Theory Ramif. 9-4:531–542, 2000) studied several classes of w-knotted objects (under the name “weakly-virtual”) and has shown them to be closely related to certain classes of knotted surfaces in $${\mathbb R}^4$$ . In this article we study finite type invariants of w-tangles and w-trivalent graphs (also referred to as w-tangled foams). Much as the spaces $${\mathcal A}$$ of chord diagrams for ordinary knotted objects are related to metrized Lie algebras, the spaces $${\mathcal A}^w$$ of “arrow diagrams” for w-knotted objects are related to not-necessarily-metrized Lie algebras. Many questions concerning w-knotted objects turn out to be equivalent to questions about Lie algebras. Most notably we find that a homomorphic universal finite type invariant of w-foams is essentially the same as a solution of the Kashiwara and Vergne (Invent. Math. 47:249–272, 1978) conjecture and much of the Alekseev and Torossian (Ann. Math. 175:415–463, 2012) work on Drinfel’d associators and Kashiwara–Vergne can be re-interpreted as a study of w-foams.
Ending Page	1586
Page Count	70
Starting Page	1517
File Format	PDF
ISSN	00255831
e-ISSN	14321807
Journal	Mathematische Annalen
Issue Number	3-4
Volume Number	367
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-05-11
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematics Knots and links in $S^3$
Content Type	Text
Resource Type	Article
Subject	Mathematics

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Finite Type Invariants of w-Knotted Objects II: Tangles, Foams and the Kashiwara-Vergne Problem

Finite type invariants of w-knotted objects II: tangles, foams and the Kashiwara–Vergne problem

Finite Type Invariants of W-Knotted Objects II: Tangles and the Kashiwara-Vergne Problem (2014)

Finite Type Invariants of w-Knotted Objects: From Alexander to Kashiwara and Vergne

Finite type invariants of w-knotted objects: from alexander to kashiwara and vergne (2010).

Finite type invariants of W-knotted Objects: From Alexander to Kashiwara and Vergne (2014)

Finite type invariants of w-knotted objects: from alexander to kashiwara and vergne (2008).

Finite type invariants of w-knotted objects: from alexander to kashiwara and vergne (2012).

Finite Type Invariants of w-Knotted Objects: From Alexander to Kashiwara and Vergne

Finite type invariants of w-knotted objects II: tangles, foams and the Kashiwara–Vergne problem

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