Configuration spaces and Vassiliev classes in any dimension.
Deformations of reducible representations of 3-manifold groups into .
Deligne-Beilinson cohomology and abelian link invariants.
Determinants of knots and Diophantine equations
Efficient formula of the colored Kauffman brackets.
End reductions, fundamental groups, and covering spaces of irreducible open 3-manifolds.
Equivalence classes of colorings
For any link and for any modulus m we introduce an equivalence relation on the set of non-trivial m-colorings of the link (an m-coloring has values in Z/mZ). Given a diagram of the link, the equivalence class of a non-trivial m-coloring is formed by each assignment of colors to the arcs of the diagram that is obtained from the former coloring by a permutation of the colors in the arcs which preserves the coloring condition at each crossing. This requirement implies topological invariance of the...
Eta invariants as sliceness obstructions and their relation to Casson-Gordon invariants.
Euclidean Mahler measure and twisted links.
Extended Bloch group and the Cheeger-Chern-Simons class.
Finite-type invariants of Legendrian knots in the 3-space: Maslov index as an order 1 invariant
We consider a contractible closure of the space of Legendrian knots in the standard contact 3-space. We show that in this context the space of finite-type complex-valued invariants of Legendrian knots is isomorphic to that of framed knots in with an extra order 1 generator (Maslov index) added.
Floer homology of surgeries on two-bridge knots.
Framed holonomic knots.
Gauge theoretic invariants of Dehn surgeries on knots.
Generating function polynomials for Legendrian links.
Geometric construction of spinors in orthogonal modular categories.
Gradients de Heegaard sous-logarithmiques d’une variété hyperbolique de dimension trois et fibres virtuelles
J. Maher a montré qu’une variété hyperbolique de dimension compacte sans bord, connexe et orientable fibre virtuellement sur le cercle si et seulement si elle admet une famille infinie de revêtements finis de genre de Heegaard borné. En s’appuyant sur la démonstration de Maher, cet article présente un théorème donnant une condition suffisante pour qu’un revêtement fini d’une variété hyperbolique compacte de dimension contienne une fibre virtuelle, qui s’exprime en fonction du degré du revêtement...
Graph Cohomology, Colored Posets and Homological Algebra in Functor Categories
The homology theory of colored posets, defined by B. Everitt and P. Turner, is generalized. Two graph categories are defined and Khovanov type graph cohomology are interpreted as Ext* groups in functor categories associated to these categories. The connection, described by J. H. Przytycki, between the Hochschild homology of an algebra and the graph cohomology, defined for the same algebra and a cyclic graph, is explained from the point of view of homological algebra in functor categories.
Gropes and the rational lift of the Kontsevich integral
We calculate the leading term of the rational lift of the Kontsevich integral, , introduced by Garoufalidis and Kricker, on the boundary of an embedded grope of class, 2n. We observe that it lies in the subspace spanned by connected diagrams of Euler degree 2n-2 and with a bead t-1 on a single edge. This places severe algebraic restrictions on the sort of knots that can bound gropes, and in particular implies the two main results of the author’s thesis [1], at least over the rationals.
Handle attaching in symplectic homology and the Chord Conjecture
Arnold conjectured that every Legendrian knot in the standard contact structure on the 3-sphere possesses a haracteristic chord with respect to any contact form. I confirm this conjecture if the know has Thurston-Bennequin invariant . More generally, existence of chords is proved for a standard Legendrian unknot on the boundary of a subcritical Stein manifold of any dimension. There is also a multiplicity result which implies in some situations existence of infinitely many chords. The proof relies...