We show that if Y is the boundary of an almost-rational plumbing, then the framed instanton Floer homology I # pY q is isomorphic to the Heegaard Floer homology y HF pY ; Cq.This class of 3-manifolds includes all Seifert fibered rational homology spheres with base orbifold S 2 (we establish the isomorphism for the remaining Seifert fibered rational homology spheres-with base RP 2 -directly).Our proof utilizes lattice homology, and relies on a decomposition theorem for instanton Floer cobordism maps recently established by Baldwin and Sivek.1 Associated to negative-definite plumbings. 2Up to orientation reversal.
Coughing is an important defensive reflex that occurs through the stimulation of a complex reflex arc. It accounts for a significant number of consultations both at the level of general practitioner and of respiratory specialists. In this review we first analyze the cough reflex under normal conditions; then we analyze the anatomy and the neuro-pathophysiology of the cough reflex arc. The aim of this review is to provide the anatomic and pathophysiologic elements of evaluation of the complex and multiple etiologies of cough.
Using the covering involution on the double branched cover of the three-sphere branched along a knot, and adapting ideas of Hendricks-Manolescu and Hendricks-Hom-Lidman, we define new knot invariants and apply them to deduce novel linear independence results in the smooth concordance group of knots.
We consider the question, asked by Friedl, Livingston and Zentner, of which sums of torus knots are concordant to alternating knots. After a brief analysis of the problem in its full generality, we focus on sums of two torus knots. We describe some effective obstructions based on Heegaard Floer homology.
Using the covering involution on the double branched cover of the three-sphere branched along a knot, and adapting ideas of Hendricks-Manolescu and Hendricks-Hom-Lidman, we define new knot invariants and apply them to deduce novel linear independence results in the smooth concordance group of knots.
We show that if $Y$ is the boundary of an almost-rational plumbing, then the framed instanton Floer homology $\smash{I^\#(Y)}$ is isomorphic to the Heegaard Floer homology $\smash{\widehat{\mathit{HF}}(Y; \mathbb{C})}$. This class of 3-manifolds includes all Seifert fibered rational homology spheres with base orbifold $S^2$ (we establish the isomorphism for the remaining Seifert fibered rational homology spheres$\unicode{x2014}$with base $\mathbb{RP}^2$$\unicode{x2014}$directly). Our proof utilizes lattice homology, and relies on a decomposition theorem for instanton Floer cobordism maps recently established by Baldwin and Sivek.
The scope of the paper is threefold. First, we build on recent work by Hayden to compute Hedden's tau-invariant $\tau_{\xi}(L)$ in the case when $\xi$ is a Stein fillable contact structure, and $L$ is a transverse link arising as the boundary of a $J$-holomorphic curve. This leads to a new proof of the relative Thom conjecture for Stein domains. Secondly, we compare the invariant $\tau_\xi$ to the Grigsby-Ruberman-Strle topological tau-invariant $\tau_{\mathfrak s}$, associated to the $\text{Spin}^c$-structure $\mathfrak s=\mathfrak s_\xi$ of the contact structure, to admit topological obstructions for a link type to contain a holomorphically fillable transverse representative. We combine the latter with a result of Mark and Tosun to confirm a conjecture of Gompf: no standardly-oriented Brieskorn homology sphere bounds a rational homology four-ball Stein filling, with any contact structure. Finally, we use our main result together with methods from lattice cohomology to compute the $\tau_{\mathfrak s}$-invariants of certain links in lens spaces, and estimate their PL slice genus.
In a recent note F. Lin showed that if a rational homology sphere $Y$ admits a taut foliation then the Heegaard Floer module $HF^-(Y)$ contains a copy of $\mathbf{F}[U]/U$ as a summand (arXiv:2309.01222). This implies that either the $L$-space conjecture is false or that Heegaard Floer homology satisfies a geography restriction. We verify that Lin's geography restriction holds for a wide class of rational homology spheres. Indeed, we show that the Heegaard Floer module $HF^-(Y)$ may satisfy a stronger geography restriction.
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