Abstract We define a new family of spectral invariants associated to certain Lagrangian links in compact and connected surfaces any genus. show that our recover the Calabi invariant Hamiltonians their limit. As applications, we resolve several open questions from topological surface dynamics continuous symplectic topology: group Hamiltonian homeomorphisms with (possibly empty) boundary is not s...

We define a broad class of local Lagrangian intersections which we call quasi-minimally degenerate (QMD) before developing techniques for studying their Floer homology. In some cases, one may think such as modeled on minimally functions defined by Kirwan. One major result this paper is: if $L_0,L_1$ are two submanifolds whose intersection decomposes into QMD sets, there is spectral sequence con...

Oriented ribbon graphs (dessins d’enfant) are graphs embedded in oriented surfaces. A quasi-tree of a ribbon graph is a spanning subgraph with one face, which is described by an ordered chord diagram. We show that for any link diagram L , there is an associated ribbon graph whose quasi-trees correspond bijectively to spanning trees of the graph obtained by checkerboard coloring L . This corresp...

We construct an explicit equivalence between the (bi)category of gl(2) webs and foams Bar-Natan Temperley-Lieb diagrams cobordisms. With this we can fix functoriality every link homology theory that factors through category. To achieve this, define web versions arc algebras their quasi-hereditary covers, which provide strictly functorial tangle homologies. Furthermore, isomorphisms these origin...

We define partial quasi-morphisms on the group of Hamiltonian diffeomorphisms cotangent bundle using spectral invariants in Lagrangian Floer homology with conormal boundary conditions, where product compatible PSS isomorphism and homological intersection is lacking.

We define Hamiltonian simplex differential graded algebras (DGA) with differentials that deform the high-energy symplectic homology differential and wrapped Floer homology differential in the cases of closed and open strings in a Liouville manifold of finite type, respectively. The order-m term in the differential is induced by varying natural degree-m coproducts over an .m 1/–simplex, where th...

The shear free condition is studied for dissipative relativistic self–gravitating fluids in the quasi–static approximation. It is shown that, in the Newtonian limit, such condition implies the linear homology law for the velocity of a fluid element,only if homology conditions are further imposed on the temperature and the emission rate.It is also shown that the shear–free plus the homogeneous e...

In this paper, we define a border operator for generalized maps, a data structure for representing cellular quasi-manifolds. The interest of this work lies in the optimization of homology computation, by using a model with less cells than models in which cells are regular ones as tetrahedra and cubes. For instance, generalized maps have been used for representing segmented images. We first defi...