Related papers: Compatibility of quantum trace and UV-IR maps
The nth relative Kauffman bracket skein modules are defined and two theorems are given relating them to the Kauffman bracket skein module of a 3-manifold. The first theorem covers the case when the 3-manifold is split along a separating…
Yang-Baxter (YB) map systems (or set-theoretic analoga of entwining YB structures) are presented. They admit zero curvature representations with spectral parameter depended Lax triples L1, L2, L3 derived from symplectic leaves of 2 x 2…
We study the stated skein modules of marked 3-manifolds. We generalize the splitting homomorphism for stated skein algebras of surfaces to a splitting homomorphism for stated skein modules of 3-manifolds. We show that there exists a…
We demonstrate that any self-adjoint coupling in a quantum graph vertex can be approximated by a family of magnetic Schroedinger operators on a tubular network built over the graph. If such a manifold has a boundary, Neumann conditions are…
The recent result of Strominger, Yau and Zaslow relating mirror symmetry to the quantum field theory notion of T-duality is reinterpreted as providing a way of geometrically characterizing which Calabi-Yau manifolds have mirror partners.…
This paper studies cutting and pasting groups (SK-groups) of pairs of manifolds. By a pair of manifolds we mean a manifold with a submanifold of strictly smaller dimension. Existing results in the unoriented category by Komiya are…
Let \Sigma_g be a closed orientable surface of genus g \geq 2 and \tau a graph on \Sigma_g with one vertex which lifts to a triangulation of the universal cover. We have shown that the cross ratio parameter space \mathcal{C}_\tau associated…
We introduce a coarse perspective on relations of the $SU(2)$-Witten-Reshetikhin-Turaev TQFT, the Weil-Petersson geometry of the Teichm\"uller space, and volumes of hyperbolic 3-manifolds. Using data from the asymptotic expansions of the…
We consider a 3-Calabi-Yau triangulated category associated to an ideal triangulation of a marked bordered surface. Using the theory of harmonic maps between Riemann surfaces, we construct a natural map from a component of the space of…
We generalize Bonahon-Wong's $\mathrm{SL}_2(\mathbb{C})$-quantum trace map to the setting of $\mathrm{SL}_3(\mathbb{C})$. More precisely, given a non-zero complex parameter $q=e^{2 \pi i \hbar}$, we associate to each isotopy class of framed…
We introduce the notion of deformed quantum vertex algebra module associated with a braiding map. We construct two families of braiding maps over the Etingof-Kazhdan quantum vertex algebras associated with the rational $R$-matrices of…
We show the Teichm\"uller space of a non-orientable surface with marked points (considered as a Klein surface) can be identified with a subspace of the Teichm\"uller space of its orientable double cover. Also, it is well known that the…
The relation between open topological strings and representation theory of symmetric quivers is explored beyond the original setting of the knot-quiver correspondence. Multiple cover generalizations of the skein relation for boundaries of…
We show that there are one-loop IR singularities arising from UV/IR mixing in noncommutative SU(N) Yang-Mills theory defined by means of the $\theta$-exact Seiberg-Witten map. This is in spite of the fact that there are no ordinary U(1)…
In this paper, we will compute the dimension of the space of spun and ordinary normal surfaces in an ideal triangulation of the interior of a compact 3-manifold with incompressible tori or Klein bottle components. Spun normal surfaces have…
We review both the construction of conformal blocks in quantum Liouville theory and the quantization of Teichm\"uller spaces as developed by Kashaev, Checkov and Fock. In both cases one assigns to a Riemann surface a Hilbert space acted on…
Classically, the dual under the Seiberg-Witten map of noncommutative U(N), {\cal N}=1 super Yang-Mills theory is a field theory with ordinary gauge symmetry whose fields carry, however, a \theta-deformed nonlinear realisation of the {\cal…
We prove a concordance version of the 4-dimensional light bulb theorem for $\pi_1$-negligible compact orientable surfaces, where there is a framed but not necessarily embedded dual sphere. That is, we show that if $F_0$ and $F_1$ are such…
This paper studies deformations and birational maps between singular moduli spaces of semistable sheaves with 2-divisible Mukai vectors on K3 surfaces. It is showed that under certain conditions, two such moduli spaces of the same dimension…
This work solves a 28-year conjecture by showing that two major invariants of smooth 4-manifolds, the shadow model (motivated by statistical mechanics [Tur91]) and the simplicial Crane-Yetter model (motivated by topological quantum field…