Related papers: An axiomatic approach to virtual chains

The knot Floer complex together with the associated concordance invariant epsilon can be used to define a filtration on the smooth concordance group. We show that the indexing set of this filtration contains the natural numbers cross the…

For any closed symplectic manifold, we show that the number of 1-periodic orbits of a nondegenerate Hamiltonian thereon is bounded from below by a version of total Betti number over Z of the ambient space taking account of the total Betti…

Two categorifications are given for the arrow polynomial, an extension of the Kauffman bracket polynomial for virtual knots. The arrow polynomial extends the bracket polynomial to infinitely many variables, each variable corresponding to an…

Floquet theory is a widely used framework to describe the dynamics of periodically-driven quantum systems. The usual set up to describe such kind of systems is to consider the effect of an external control with a definite period in time…

In the paper of Yu. A. Mikhalchishina for an arbitrary virtual link $L$ three groups $G_{1,r}(L)$, $r>0$, $G_{2}(L)$ and $G_{3}(L)$ were defined. In the present paper these groups for the virtual trefoil are investigated. The structure of…

Virtual links were introduced by Kauffman in 1999. We characterize the virtual link invariants that are partition functions of vertex models (as considered by de la Harpe and Jones), both in the real and in the complex case. We show that…

A virtual $n$-string $\alpha$ is a collection of $n$ oriented smooth generic loops on a surface $M$. A stabilization of $\alpha$ is a surgery that results in attaching a handle to $M$ along disks avoiding $\alpha$, and the inverse operation…

We characterize virtual double categories of enriched categories, functors, and profunctors by introducing a new notion of double-categorical colimits. Our characterization is strict in the sense that it is up to equivalence between virtual…

In various situations in Floer theory, one extracts homological invariants from "Morse-Bott" data in which the "critical set" is a union of manifolds, and the moduli spaces of "flow lines" have evaluation maps taking values in the critical…

The authors previous derivation of a variational principle from the total work functional, as a generalization of the first variation of an action functional, is extended by deriving a corresponding generalization of the Hamiltonian…

We give a purely combinatorial proof of a K\"{u}nneth formula for the minus version of knot Floer homology of connected sums by constructing a quasi-isomorphism of grid chain complexes. The quasi-isomorphism naturally deduces that the…

In a first part we propose an introduction to multisymplectic formalisms, which are generalisations of Hamilton's formulation of Mechanics to the calculus of variations with several variables: we give some physical motivations, related to…

We construct a version of Hamiltonian Floer Homology based on the notion of a semi-infinite cycle. As an application, we provide a new proof for the existence of critical points of the action functional.

We construct the vortex Floer homology group $VHF (M,\mu;H)$ for an aspherical Hamiltonian $G$-manifold $(M, \omega)$ with moment map $\mu$ and a class of $G$-invariant Hamiltonian loop $H_t$, following the proposal of [3]. This is a…

A Hamiltonian cycle of a graph is a closed path that visits each site once and only once. I study a field theoretic representation for the number of Hamiltonian cycles for arbitrary graphs. By integrating out quadratic fluctuations around…

Floer field theory is a construction principle for e.g. 3-manifold invariants via decomposition in a bordism category and a functor to the symplectic category, and is conjectured to have natural 4-dimensional extensions. This survey…

This thesis is divided into three parts. In the first part, we give an introduction to J. Harrison's theory of differential chains. In the second part, we apply these tools to generalize the Cauchy theorems in complex analysis. Instead of…

We develop the theory of relative monads and relative adjunctions in a virtual equipment, extending the theory of monads and adjunctions in a 2-category. The theory of relative comonads and relative coadjunctions follows by duality. While…

We introduce the notions "virtual automorphism group" of a minimal flow and "semi-regular flow" and investigate the relationship between the virtual and actual group of automorphisms.

We define new notions of groups of virtual and welded knots (or links) and we study their relations with other invariants, in particular the Kauffman group of a virtual knot.