Related papers: An axiomatic approach to virtual chains

Mirror symmetry for higher genus curves is usually formulated and studied in terms of Landau-Ginzburg models; however the critical locus of the superpotential is arguably of greater intrinsic relevance to mirror symmetry than the whole…

Equivariant singular instanton Floer theory is a framework that associates to a knot in an integer homology 3-sphere a suite of homological invariants that are derived from circle-equivariant Morse-Floer theory of a Chern-Simons functional…

Various models of $(\infty,1)$-categories, including quasi-categories, complete Segal spaces, Segal categories, and naturally marked simplicial sets can be considered as the objects of an $\infty$-cosmos. In a generic $\infty$-cosmos, whose…

The 2016 papers of J. Solomon and S. Tukachinsky use bounding chains in Fukaya's $A_{\infty}$-algebras to define numerical disk counts relative to a Lagrangian under certain regularity assumptions on the moduli spaces of disks. We present a…

We present a new theoretical and numerical assessment methodology for a one-dimensional process chain with general applicability to management problems such as the optimization of decision chains or production chains. The process is thereby…

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…

The concept of a variance on a category is introduced as a two-sided strict factorization system. By employing variances, we define functors of variance in a more general setting than is usually considered, thereby eliminating the need for…

A pseudodiagram is a diagram of a knot with some crossing information missing. We review and expand the theory of pseudodiagrams introduced by R. Hanaki. We then extend this theory to the realm of virtual knots, a generalization of knots.…

Ongoing work in quantum information emphasises the need for a structural understanding of quantum speedups: in this work, we focus on the quantum Fourier transform and the structures in quantum theory that enable it. We elucidate a general…

We introduce the notion of a diagram category and discuss its application to the invariant theory of classical groups and super groups, with some indications concerning extensions to quantum groups and quantum super groups. Tensor functors…

We construct an unwrapped Floer theory for bundles of Liouville sectors. In particular, we construct a compatible collection of unwrapped Fukaya categories of fibers of a Liouville bundle, and prove that the two natural constructions of…

For any virtual link, a class of new links can be defined called stacks, in which copies of the virtual link are placed on top of one another. The resulting virtual link depends only on the virtual isotopy class of the original link, and…

A symplectic manifold gives rise to a triangulated A-infinity category, the derived Fukaya category, which encodes information on Lagrangian submanifolds and dynamics as probed by Floer cohomology. This survey aims to give some insight into…

Given a Lagrangian fibration, we provide a natural construction of a mirror Landau-Ginzburg model consisting of a rigid analytic space, a superpotential function, and a dual fibration based on Fukaya's family Floer theory. The mirror in the…

We resolve the long-standing problem of constructing the action of the operad of framed (stable) genus-$0$ curves on Hamiltonian Floer theory; this operad is equivalent to the framed $E_2$ operad. We formulate the construction in the…

This paper contains a categorification of the sl(k) link invariant using parabolic singular blocks of category O. Our approach is intended to be as elementary as possible, providing combinatorial proofs of the main results of Sussan. We…

This note is intended to be a friendly introduction to virtual classes. We review virtual classes and we give a number of properties and applications. We also include a new virtual push-forward theorem and many computations of virtual…

In the framework of chiral perturbation theory virtual photons are included. We calculate the divergences of the generating functional to one loop and determine the structure of the local action that incorporates the counterterms which…

A formulation of singular classical theories (determined by degenerate Lagrangians) without constraints is presented. A partial Hamiltonian formalism in the phase space having an initially arbitrary number of momenta (which can be smaller…

For an aspherical symplectic manifold, closed or with convex contact boundary, and with vanishing first Chern class, a Floer chain complex is defined for Hamiltonians linear at infinity with coefficients in the group ring of the fundamental…