Related papers: Strong L-spaces and left orderability

We classify connected sums of three-dimensional lens spaces which smoothly bound rational homology balls. We use this result to determine the order of each lens space in the group of rational homology 3-spheres up to rational homology…

We show that if $V^3$ is a handlebody in $\R^3$, with curves $J_1, ..., J_g \subset \partial V$ which are the attaching curves for a Heegaard splitting of a homology sphere, then there exists a homeomorphism $h\colon V \to V$ so that each…

We classify genus-two L-space knots in the Poincar\'e homology sphere. This leads to the second knot Floer homology detection result for a knot of genus at least two, and the first such result outside of $S^3$. The argument uses the theory…

We consider the question of when a rational homology 3-sphere is rational homology cobordant to a connected sum of lens spaces. We prove that every rational homology cobordism class in the subgroup generated by lens spaces is represented by…

We compute different versions of link Floer homology $HFL^{-}$ and $\widehat{HFL}$ for any $L$-space link with two components. The main approach is to compute the $h$-function of the filtered chain complex which is determined by the…

We show that the Seifert-Weber dodecahedral space $\mathsf{SW}$ is an $L$-space. The proof builds on our work relating Floer homology and spectral geometry of hyperbolic three-manifolds. A direct application of our previous techniques runs…

Hedden defined two knots in each lens space that, through analogies with their knot Floer homology and doubly pointed Heegaard diagrams of genus one, may be viewed as generalizations of the two trefoils in S^3. Rasmussen shows that when the…

Let M be a closed, connected and oriented 3-manifold. This article is the first of a five part series that constructs an isomorphism between the Heegaard Floer homology groups of M and the corresponding Seiberg-Witten Floer homology groups…

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…

The notion of L-homologies (of double complexes) as proposed in this paper extends the notion of classical horizontal and vertical homologies, along with two other new homologies introduced in the homological diagram lemma called salamander…

In this paper, we define real link Floer homology for strongly invertible and doubly periodic links in closed real $3$-manifolds with connected fixed sets, which generalizes real Heegaard Floer homology and real sutured Heegaard Floer…

A knot in the 3-sphere is called an L-space knot if it admits a nontrivial Dehn surgery yielding an L-space, i.e. a rational homology 3-sphere with the smallest possible Heegaard Floer homology. Given a knot K, take an unknotted circle c…

We show that the space of left-orderings of a countable virtually solvable group is either finite or homeomorphic to a Cantor set. We also provide an explicit description of the space of left-orderings of $SOL=\Z^2\rtimes_T\Z$.

A rational homology sphere whose Heegaard Floer homology is the same as that of a lens space is called an L-space. We classify pretzel knots with any number of tangles which admit L-space surgeries. This rests on Gabai's classification of…

We consider a class of manifolds with torus boundary admitting bordered Heegaard Floer homology of a particularly simple form, namely, the type D structure may be described graphically by a disjoint union of loops. We develop a calculus for…

We calculate the Heegaard Floer homologies for three-manifolds obtained by plumbings of spheres specified by certain graphs. Our class of graphs is sufficiently large to describe, for example, all Seifert fibered rational homology spheres.…

For each $m\geq0$ and any prime $p\equiv3\ \mathrm{(mod \ 4)}$, we construct strongly chiral rational homology $(4m+3)$-spheres, which have real hyperbolic fundamental groups and only non-zero integral intermediate homology groups…

Greene, Lewallen and Vafaee characterized $(1,1)$ L-space knots in $S^3$ and lens space in the notation of coherent reduced $(1,1)$-diagrams. We analyze these diagrams, and deduce an explicit description of these knots. With the new…

A topological space $X$ is $strongly$ $rigid$ if each non-constant continuous map $f:X\to X$ is the identity map of $X$. A Hausdorff topological space $X$ is called $Brown$ if for any nonempty open sets $U,V\subseteq X$ the intersection…

In this paper we prove a group theoretic analogue of the well known local nilpotence theorem for sandwich Lie algebras due to Kostrikin and Zel'manov. We introduce the notion of a strong left 3-Engel element of a group G and show that these…