Zobrazeno 1 - 10
of 177
pro vyhledávání: '"Ekholm, Tobias"'
HOMFLYPT polynomials of knots in the 3-sphere in symmetric representations satisfy recursion relations. Their geometric origin is holomorphic curves at infinity on knot conormals that determine a $D$-module with characteristic variety the Legendrian
Externí odkaz:
http://arxiv.org/abs/2407.09836
Autor:
Ekholm, Tobias, Shende, Vivek
We construct a class of perturbations of the Cauchy-Riemann equation for maps from curves to a Calabi-Yau threefold, allowing Maslov zero Lagrangian boundary conditions. Our perturbations vanish on components of zero symplectic area. For generic 1-pa
Externí odkaz:
http://arxiv.org/abs/2406.00890
Autor:
Ekholm, Tobias, Shende, Vivek
When a Gromov limit of embedded holomorphic curves is constant on some component of the domain, the non-collapsed component must exhibit some degenerate behavior at the attaching points, such as high multiplicity or vanishing of the holomorphic deriv
Externí odkaz:
http://arxiv.org/abs/2212.05835
Autor:
Ekholm, Tobias, Gruen, Angus, Gukov, Sergei, Kucharski, Piotr, Park, Sunghyuk, Stošić, Marko, Sułkowski, Piotr
Publikováno v:
J. Geom. Phys. 177 (2022), 104520
We generalize the $F_K$ invariant, i.e. $\widehat{Z}$ for the complement of a knot $K$ in the 3-sphere, the knots-quivers correspondence, and $A$-polynomials of knots, and find several interconnections between them. We associate an $F_K$ invariant to
Externí odkaz:
http://arxiv.org/abs/2110.13768
We conjecture a relation between generalized quiver partition functions and generating functions for symmetrically colored HOMFLY-PT polynomials and corresponding HOMFLY-PT homology Poincar\'e polynomials of a knot $K$. We interpret the generalized q
Externí odkaz:
http://arxiv.org/abs/2108.12645
Autor:
Asplund, Johan, Ekholm, Tobias
Publikováno v:
J. Symplectic Geom. 20(3), 509-559, 2022
The Chekanov-Eliashberg dg-algebra is a holomorphic curve invariant associated to Legendrian submanifolds of a contact manifold. We extend the definition to Legendrian embeddings of skeleta of Weinstein manifolds. Via Legendrian surgery, the new defi
Externí odkaz:
http://arxiv.org/abs/2102.04858
Autor:
Ekholm, Tobias, Shende, Vivek
We compute the contribution of all multiple covers of an isolated rigid embedded holomorphic annulus, stretching between Lagrangians, to the skein-valued count of open holomorphic curves in a Calabi-Yau 3-fold. The result agrees with the predictions
Externí odkaz:
http://arxiv.org/abs/2101.00619
Autor:
Ekholm, Tobias, Shende, Vivek
We determine the skein-valued Gromov-Witten partition function for a single toric Lagrangian brane in $\mathbb{C}^3$ or the resolved conifold. We first show geometrically they must satisfy a certain skein-theoretic recursion, and then solve this equa
Externí odkaz:
http://arxiv.org/abs/2012.15366
Autor:
Ekholm, Tobias, Gruen, Angus, Gukov, Sergei, Kucharski, Piotr, Park, Sunghyuk, Sułkowski, Piotr
Reducing a 6d fivebrane theory on a 3-manifold $Y$ gives a $q$-series 3-manifold invariant $\widehat{Z}(Y)$. We analyse the large-$N$ behaviour of $F_K=\widehat{Z}(M_K)$, where $M_K$ is the complement of a knot $K$ in the 3-sphere, and explore the re
Externí odkaz:
http://arxiv.org/abs/2005.13349
Autor:
Diogo, Luís, Ekholm, Tobias
The augmentation variety of a knot is the locus, in the 3-dimensional coefficient space of the knot contact homology dg-algebra, where the algebra admits a unital chain map to the complex numbers. We explain how to express the Alexander polynomial of
Externí odkaz:
http://arxiv.org/abs/2005.09733