Zobrazeno 1 - 10
of 116
pro vyhledávání: '"Manolescu, Ciprian"'
We apply Bayesian optimization and reinforcement learning to a problem in topology: the question of when a knot bounds a ribbon disk. This question is relevant in an approach to disproving the four-dimensional smooth Poincar\'e conjecture; using our
Externí odkaz:
http://arxiv.org/abs/2304.09304
Autor:
Manolescu, Ciprian, Willis, Michael
Asaeda-Przytycki-Sikora, Manturov, and Gabrov\v{s}ek extended Khovanov homology to links in $\mathbb{RP}^3$. We construct a Lee-type deformation of their theory, and use it to define an analogue of Rasmussen's s-invariant in this setting. We show tha
Externí odkaz:
http://arxiv.org/abs/2301.09764
The skein lasagna module is an extension of Khovanov-Rozansky homology to the setting of a four-manifold and a link in its boundary. This invariant plays the role of the Hilbert space of an associated fully extended (4+epsilon)-dimensional TQFT. We g
Externí odkaz:
http://arxiv.org/abs/2206.04616
Autor:
Manolescu, Ciprian, Sarkar, Sucharit
Given a grid diagram for a knot or link K in $S^3$, we construct a spectrum whose homology is the knot Floer homology of K. We conjecture that the homotopy type of the spectrum is an invariant of K. Our construction does not use holomorphic geometry,
Externí odkaz:
http://arxiv.org/abs/2108.13566
Autor:
Manolescu, Ciprian, Piccirillo, Lisa
One strategy for distinguishing smooth structures on closed $4$-manifolds is to produce a knot $K$ in $S^3$ that is slice in one smooth filling $W$ of $S^3$ but not slice in some homeomorphic smooth filling $W'$. In this paper we explore how $0$-surg
Externí odkaz:
http://arxiv.org/abs/2102.04391
Given a closed four-manifold $X$ with an indefinite intersection form, we consider smoothly embedded surfaces in $X \setminus $int$(B^4)$, with boundary a knot $K \subset S^3$. We give several methods to bound the genus of such surfaces in a fixed ho
Externí odkaz:
http://arxiv.org/abs/2012.12270
Autor:
Manolescu, Ciprian, Neithalath, Ikshu
Morrison, Walker, and Wedrich used the blob complex to construct a generalization of Khovanov-Rozansky homology to links in the boundary of a 4-manifold. The degree zero part of their theory, called the skein lasagna module, admits an elementary defi
Externí odkaz:
http://arxiv.org/abs/2009.08520
We extend the definition of Khovanov-Lee homology to links in connected sums of $S^1 \times S^2$'s, and construct a Rasmussen-type invariant for null-homologous links in these manifolds. For certain links in $S^1 \times S^2$, we compute the invariant
Externí odkaz:
http://arxiv.org/abs/1910.08195
Publikováno v:
In Advances in Mathematics 15 July 2023 425
Autor:
Gukov, Sergei, Manolescu, Ciprian
The physical 3d $\mathcal{N}=2$ theory T[Y] was previously used to predict the existence of some 3-manifold invariants $\hat{Z}_{a}(q)$ that take the form of power series with integer coefficients, converging in the unit disk. Their radial limits at
Externí odkaz:
http://arxiv.org/abs/1904.06057