Related papers: A bordered HF- algebra for the torus

Starting from a Heegaard splitting of a three-manifold, we use Lagrangian Floer homology to construct a three-manifold invariant, in the form of a relatively Z/8-graded abelian group. Our motivation is to have a well-defined symplectic side…

A brief survey of some aspects of noetherian Hopf algebras is given, concentrating on structure, homology, and classification, and accompanied by a panoply of open problems.

This work is a sequel to [arXiv:2410.18575], and a third and final installment of the program initiated in [arXiv:2311.18302]. We show how, via a 3d gauged Landau-Ginzburg model interpretation of certain topologically-twisted 5d…

We show that $\tau$-tilting finite simply connected algebras are representation-finite. Then, some related algebras are considered, including iterated tilted algebras, tubular algebras and so on. We also prove that the $\tau$-tilting…

We show that the number of genus $g$ embedded minimal surfaces in $\mathbb{S}^3$ tends to infinity as $g\rightarrow\infty$. The surfaces we construct resemble doublings of the Clifford torus with curvature blowing up along torus knots as…

Given a closed symplectic manifold $(M,\omega)$ we introduce a certain quantity associated to a tuple of conjugacy classes in the universal cover of the group ${\hbox{\it Ham}} (M,\omega)$ by means of the Hofer metric on ${\hbox{\it Ham}}…

We study local algebras, which are structures similar to $\mathbb{Z}$-graded algebras concentrated in degrees $-1,0,1$, but without a product defined for pairs of elements at the same degree $\pm1$. To any triple consisting of a Kac-Moody…

We show how one can define novel gauge-theoretic Floer homologies of four, three, and two-manifolds from the physics of a certain topologically-twisted 5d ${\cal N}=2$ gauge theory via its supersymmetric quantum mechanics interpretation.…

The exterior algebra $E$ on a finite-rank free module $V$ carries a $\mathbb{Z}/2$-grading and an increasing filtration, and the $\mathbb{Z}/2$-graded filtered deformations of $E$ as an associative algebra are the familiar Clifford…

For an algebraic torus $S$, Blinstein and Merkurjev have given an estimate of $3$-th unramified cohomology $\bar{H}^3_{nr}(F(S),\mathbb Q/\mathbb Z(2))$ obtained from a flasque resolution of $S$. Based on their work, for the norm one torus…

In this paper we define, for each aspherical orientable 3-manifold $M$ endowed with a \emph{torus splitting} $\c{T}$, a 2-dimensional fundamental $l_1$-class $[M]^{\c{T}}$ whose $l_1$-norm has similar properties as the Gromov simplicial…

In this paper we refine the main result of a previous paper of the author with Grimeland on derived invariants of surface algebras. We restrict to the case where the surface is a torus with one boundary component and give an easily…

Geometrization says `` any closed oriented three-manifold which is prime (not a connected sum) carries one of the eight Thurston geometries OR it has incompressible torus walls whose complementary components each carry one of four…

The representations of the pointed Hopf algebras $U$ and $\su$ are described, where $U$ and $\su$ can be regarded as deformations of the usual quantized enveloping algebras $U_q(\mathfrak{sl}(3))$ and the small quantum groups respectively.…

After embedding the objects quasifolds into the category {Diffeology}, we associate a C*-agebra with every atlas of any quasifold, and show how different atlases give Morita equivalent algebras. This builds a new bridge between diffeology…

We construct a PROP which encodes 2D-TQFTs with a grading. This defines a graded Frobenius algebra as algebras over this PROP. We also give a description of graded Frobenius algebras in terms of maps and relations. This structure naturally…

We construct open-closed maps on various versions of Hochschild and cyclic homology of the Fukaya $A_\infty$ algebra of a Lagrangian submanifold modeled on differential forms. The $A_\infty$ algebra may be curved. Properties analogous to…

An algebra is said to be \emph{$\tau$-tilting finite} provided it has only a finite number of $\tau$-rigid objects up to isomorphism. We associate a category to each such algebra. The objects are the wide subcategories of its category of…

For a locally compact Hausdorff semigroup S, the $L^\infty$ representation algebra R(S) was extensively studied by Dunkl and Ramirez. The Fourier-Stieltjes algebra F(S) of a topological semigroup was studied by Lau. The aim of this paper is…

Let $(M,\omega_M)$ be a monotone or negatively monotone symplectic manifold, or a Weinstein manifold. One can construct an "action" of $H^1(M,\mathbb{G}_m)$ on the Fukaya category (wrapped Fukaya category in the exact case) that reflects…