Three-dimensional topological field theory and symplectic algebraic geometry I (2008)
Kapustin, Anton, Rozansky, Lev, Saulina, Natalia
We study boundary conditions and defects in a three-dimensional topological sigma-model with a complex symplectic target space X (the Rozansky-Witten model). We show that boundary conditions...
Virtual crossings, convolutions and a categorification of the SO(2N) Kauffman polynomial (2007)
Khovanov, Mikhail, Rozansky, Lev
We suggest a categorification procedure for the SO(2N) one-variable specialization of the two-variable Kauffman polynomial. The construction has many similarities with the HOMFLYPT categorification:...
Matrix factorizations and link homology II (2005)
Khovanov, Mikhail, Rozansky, Lev
To a presentation of an oriented link as the closure of a braid we assign a complex of bigraded vector spaces. The Euler characteristic of this complex (and of its triply-graded cohomology groups) is...
Matrix factorizations and link homology (2004)
Khovanov, Mikhail, Rozansky, Lev
For each positive integer n the HOMFLY polynomial of links specializes to a one-variable polynomial that can be recovered from the representation theory of quantum sl(n). For each such n we build a...
The Arhus Integral Of Rational Homology 3-Spheres Iii: (2003)
Dror Bar-natan, Stavros Garoufalidis, Lev Rozansky, P. Thurston
Continuing the work started in [ A-I] and [ A-II], we prove the relationship between the Arhus integral and the invariant (henceforth called LMO) de ned by T.Q.T. Le, J. Murakami and T. Ohtsuki in...
Dror Bar-natan, Stavros Garoufalidis, Lev Rozansky, P. Thurston
Path integrals do not really exist, but it is very useful to dream that they do and gure out the consequences. Apart from describing much of the physical world as we now know it, these dreams also...
The Arhus Integral Of Rational Homology 3-Spheres Ii: (2002)
Dror Bar-natan, Stavros Garoufalidis, Lev Rozansky, P. Thurston
We continue the work started in [ A-I], and prove the invariance and universality in the class of nite type invariants of the object de ned and motivated there, namely the Arhus integral of rational...
The loop expansion of the Kontsevich integral, the null move and S-equivalence (2000)
Garoufalidis, Stavros, Rozansky, Lev
This is a substantially revised version. The Kontsevich integral of a knot is a graph-valued invariant which (when graded by the Vassiliev degree of graphs) is characterized by a universal property;...
Dror Bar-natan, Stavros Garoufalidis, Lev Rozansky, P. Thurston
Path integrals do not really exist, but it is very useful to dream that they do, and figure out the consequences. Apart from describing much of the physical world as we now know it, these dreams also...
Wheels, Wheeling, And The Kontsevich Integral Of The Unknot (1999)
Dror Bar-natan, Stavros Garoufalidis, Lev Rozansky, P. Thurston
. We conjecture an exact formula for the Kontsevich integral of the unknot, and also conjecture a formula (also conjectured independently by Deligne [De]) for the relation between the two natural...
Witten–Reshetikhin–Turaev Invariants of¶Seifert Manifolds (1999)
For Seifert homology spheres, we derive a holomorphic function of K whose value at integer K is the sl 2 Witten–Reshetikhin–Turaev invariant, Z K , at q= exp 2π i / K . This function is...
Dror Bar-natan, Stavros Garoufalidis, Lev Rozansky, P. Thurston
. Continuing the work started in [ A-I] and [ A-II], we prove the relationship between the Arhus integral and the invariant (henceforth called LMO) dened by T.Q.T. Le, J. Murakami and T. Ohtsuki in...
Wheels, Wheeling, And The Kontsevich Integral Of The Unknot (1999)
Dror Bar-natan, Stavros Garoufalidis, Lev Rozansky, P. Thurston
. We conjecture an exact formula for the Kontsevich integral of the unknot, and also conjecture a formula (also conjectured independently by Deligne [De]) for the relation between the two natural...
Dror Bar-natan, Stavros Garoufalidis, Lev Rozansky, P. Thurston
. Continuing the work started in [ A-I] and [ A-II], we prove the relationship between the Arhus integral and the invariantOmega (henceforth called LMO) defined by T.Q.T. Le, J. Murakami and T....
Bar-Natan, Dror, Garoufalidis, Stavros, Rozansky, Lev, Thurston, Dylan P.
Continuing the work started in Part I and II of this series (see q-alg/9706004 and math.QA/9801049), we prove the relationship between the Aarhus integral and the invariant $\Omega$ (henceforth...
The Aarhus integral of rational homology 3-spheres II: Invariance and universality (1998)
Bar-Natan, Dror, Garoufalidis, Stavros, Rozansky, Lev, Thurston, Dylan
We continue the work started in part I (q-alg/9706004) and prove the invariance and universality in the class of finite type invariants of the object defined and motivated there, namely the Aarhus...
Bar-Natan, Dror, Garoufalidis, Stavros, Rozansky, Lev, Thurston, Dylan P.
Path integrals don't really exist, but it is very useful to dream that they do exist, and figure out the consequences. Apart from describing much of the physical world as we now know it, these dreams...
Wheels, Wheeling, And The Kontsevich Integral Of The Unknot (1997)
Dror Bar-natan, Stavros Garoufalidis, Lev Rozansky, P. Thurston
. We mix together the Kontsevich integral, chord diagrams, Chinese characters, the Reshetikhin-Turaev knot invariants, the Poincare-Birkhoff-Witt theorem, the HarishChandra isomorphism, the Duflo...
Wheels, Wheeling, and the Kontsevich Integral of the Unknot (1997)
Bar-Natan, Dror, Garoufalidis, Stavros, Rozansky, Lev, Thurston, Dylan P.
We conjecture an exact formula for the Kontsevich integral of the unknot, and also conjecture a formula (also conjectured independently by Deligne) for the relation between the two natural products...
We use Feynman diagrams to prove a formula for the Jones polynomial of a link derived recently by N.~Reshetikhin. This formula presents the colored Jones polynomial as an integral over the coadjoint...
We extend the results of our previous paper from knots to links by using a formula for the Jones polynomial of a link derived recently by N. Reshetikhin. We illustrate this formula by an example of a...
Witten's Invariant of 3-Dimensional Manifolds: Loop Expansion and Surgery Calculus (1994)
We review two different methods of calculating Witten's invariant: a stationary phase approximation and a surgery calculus. We give a detailed description of the 1-loop approximation formula for...
We use the Chern-Simons quantum field theory in order to prove a recently conjectured limitation on the 1/K expansion of the Jones polynomial of a knot and its relation to the Alexander polynomial....
A Large k Asymptotics of Witten's Invariant of Seifert Manifolds (1993)
We calculate a large $k$ asymptotic expansion of the exact surgery formula for Witten's $SU(2)$ invariant of Seifert manifolds. The contributions of all flat connections are identified. An agreement...
Reidemeister torsion, the Alexander polynomial and $U(1,1)$ Chern-Simons theory (1992)
Rozansky, Lev, Saleur, Herbert
We show that the $U(1,1)$ (super) Chern Simons theory is one loop exact. This provides a direct proof of the relation between the Alexander polynomial and analytic and Reidemeister torsion. We then...
R-matrix Approach to Quantum Superalgebras su_{q}(m|n) (1992)
Chang, D., Phillips, I., Rozansky, Lev
Quantum superalgebras $su_{q}(m\mid n)$ are studied in the framework of $R$-matrix formalism. Explicit parametrization of $L^{(+)}$ and $L^{(-)}$ matrices in terms of $su_{q}(m\mid n)$ generators are...
Rozansky, Lev, Saleur, Herbert
We carry on the study of the Alexander Conway invariant from the quantum field theory point of view started in \cite{RS91}. We first discuss in details $S$ and $T$ matrices for the $U(1,1)$ super WZW...
The Århus Integral Of Rational Homology 3-Spheres II: Invariance And Universality (1970)
Dror Bar-natan, Stavros Garoufalidis, Lev Rozansky, P. Thurston
. We continue the work started in [ A-I], and prove the invariance and universality in the class of finite type invariants of the object defined and motivated there, namely the Arhus integral of...
Dror Bar-natan, Stavros Garoufalidis, Lev Rozansky, P. Thurston
. Path integrals don't really exist, but it is very useful to dream that they do exist, and figure out the consequences. Apart from describing much of the physical world as we now know it, these...