Results 11 to 20 of about 40 (38)
From zero surgeries to candidates for exotic definite 4‐manifolds
Journal of the London Mathematical Society, Volume 108, Issue 5, Page 2001-2036, November 2023., 2023 Abstract One strategy for distinguishing smooth structures on closed 4‐manifolds is to produce a knot K$K$ in S3$S^3$ that is slice in one smooth filling W$W$ of S3$S^3$ but not slice in some homeomorphic smooth filling W′$W^{\prime }$. In this paper, we explore how 0‐surgery homeomorphisms can be used to potentially construct exotic pairs of this form.
Ciprian Manolescu, Lisa Piccirillo
wiley +1 more source
Lagrangian cobordism functor in microlocal sheaf theory I
Journal of Topology, Volume 16, Issue 3, Page 1113-1166, September 2023., 2023 Abstract Let Λ±$\Lambda _\pm$ be Legendrian submanifolds in the cosphere bundle T∗,∞M$T^{*,\infty }M$. Given a Lagrangian cobordism L$L$ of Legendrians from Λ−$\Lambda _-$ to Λ+$\Lambda _+$, we construct a functor ΦL*:ShΛ+c(M)→ShΛ−c(M)⊗C−*(Ω*Λ−)C−*(Ω*L)${\mathrm{\Phi}}_{L}^{\ast}:{{\rm Sh}}_{{\mathrm{\Lambda}}_{+}}^{c}(M)\to {{\rm Sh}}_{{\mathrm ...
Wenyuan Li
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Journal of Topology, Volume 15, Issue 4, Page 2216-2269, December 2022., 2022 Abstract We study relative symplectic cobordisms between contact submanifolds, and in particular relative symplectic cobordisms to the empty set, that we call hats. While we make some observations in higher dimensions, we focus on the case of transverse knots in the standard 3‐sphere, and hats in blow‐ups of the (punctured) complex projective planes ...
John B. Etnyre, Marco Golla
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New quantum obstructions to sliceness
Proceedings of the London Mathematical Society, Volume 112, Issue 1, Page 81-114, January 2016., 2016 It is well known that generic perturbations of the complex Frobenius algebra used to define Khovanov cohomology each give rise to Rasmussen's concordance invariant s. This gives a concordance homomorphism to the integers and a strong lower bound on the smooth slice genus of a knot.
Lukas Lewark, Andrew Lobb
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Fortschritte der Physik, Volume 74, Issue 4, April 2026.Abstract String theory has strong implications for cosmology, implying the absence of a cosmological constant, ruling out single‐field slow‐roll inflation, and that black holes decay. The origins of these statements are elucidated within the string‐theoretical swampland programme.
Kay Lehnert
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Local equivalence and refinements of Rasmussen's s‐invariant
Journal of Topology, Volume 19, Issue 1, March 2026.Abstract Inspired by the notions of local equivalence in monopole and Heegaard Floer homology, we introduce a version of local equivalence that combines odd Khovanov homology with equivariant even Khovanov homology into an algebraic package called a local even–odd (LEO) triple.
Nathan M. Dunfield +2 more
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Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.Abstract We classify fibered ribbon pretzel knots up to mutation. The classification is complete, except perhaps for members of Lecuona's “exceptional” family of Lecuona [Algebr. Geom. Topol. 15 (2015), no. 4, 2133–2173]. The result is obtained by combining lattice embedding techniques with Gabai's classification of fibered pretzel knots, and ...
Ana G. Lecuona, Andy Wand
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Lagrangian approximation of totally real concordances
Proceedings of the London Mathematical Society, Volume 130, Issue 4, April 2025.Abstract We show that a two‐dimensional totally real concordance can be approximated by a Lagrangian concordance whose Legendrian boundary has been stabilised both positively and negatively sufficiently many times. The main applications that we provide are constructions of knotted Lagrangian concordances in arbitrary four‐dimensional symplectisations ...
Georgios Dimitroglou Rizell
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Equivariant algebraic concordance of strongly invertible knots
Journal of Topology, Volume 17, Issue 4, December 2024.Abstract By considering a particular type of invariant Seifert surfaces we define a homomorphism Φ$\Phi$ from the (topological) equivariant concordance group of directed strongly invertible knots C∼$\widetilde{\mathcal {C}}$ to a new equivariant algebraic concordance group G∼Z$\widetilde{\mathcal {G}}^\mathbb {Z}$.
Alessio Di Prisa
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Stabilization distance bounds from link Floer homology
Journal of Topology, Volume 17, Issue 2, June 2024.Abstract We consider the set of connected surfaces in the 4‐ball with boundary a fixed knot in the 3‐sphere. We define the stabilization distance between two surfaces as the minimal g$g$ such that we can get from one to the other using stabilizations and destabilizations through surfaces of genus at most g$g$.
András Juhász, Ian Zemke
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