Related papers: Symplectomorphisms and discrete braid invariants

Let $M$ be a smooth closed orientable surface and $F=F_{p,q,r}$ be the space of Morse functions on $M$ having exactly $p$ critical points of local minima, $q\ge1$ saddle critical points, and $r$ critical points of local maxima, moreover all…

Bifurcation characterizes the qualitative changes in parameterized dynamical systems and is one of the major topics in the field. In this work, we study combinatorial bifurcations within the framework of combinatorial dynamical systems -- a…

Friedman and Morgan made the "speculation" that deformation equivalence and diffeomorphism should coincide for algebraic surfaces. Counterexamples, for the hitherto open case of surfaces of general type, have been given in the last years by…

We attach to any linear endomorphism f of any vector space V a structure of prelie algebra on the shuffle algebra T(V); we describe its enveloping algebra, the dual Hopf algebra and the associated group of characters. For f=Id\_V, we find…

We extend Donaldson's asymptotically holomorphic techniques to symplectic orbifolds. More precisely, given a symplectic orbifold such that the symplectic form defines an integer cohomology class, we prove that there exist sections of large…

The notion of a holomorphically symplectic manifold can be generalized to the singular one. This paper studies the birational contraction maps between symplectic varieties, and then describes the deformation of a symplectic variety which…

We elaborate a new method for constructing traces of quadratic forms in the framework of Hilbert and Dirichlet spaces. Our method relies on monotone convergence of quadratic forms and the canonical decomposition into regular and singular…

In the present article we study the periodic structure of some well-known classes of $C^1$ self-maps on the product of spheres of different dimensions: transversal maps, Morse-Smale diffeomorphisms and maps with all its periodic points…

Area preserving diffeomorphisms of a 2-d compact Riemannian manifold with or without boundary are studied. We find two classes of decompositions of a Riemannian metric, namely, h- and g-decomposition, that help to formulate a gravitational…

This paper is a following to math.RT/0410454. For a finite group of Lie type we study the endomorphisms, commuting with the group action, of a Deligne-Lusztig variety associated to a regular element of the Weyl group. We state some general…

In this work we relate the known results about the homotopy type of classifying spaces for smooth foliations, with the homology and cohomology of the discrete group of diffeomorphisms of a smooth compact connected oriented manifold. The…

We establish a connection between Gromov-Witten invariants and the number of fixed points of Hamiltonian diffeomorphisms on a closed rational symplectic manifold via deformed Hamiltonian spectral invariants. We generalize Givental's…

In this paper we determine for relatively minimal elliptic surfaces with positive Euler number the image of the natural representation of the group of orientation preserving self-diffeomorphisms on $\Hbar$, the second homology group reduced…

Motivated by the study of the recurrent orbits in a Morse set of a Morse decomposition, we introduce the concept of Morse predecomposition of an isolated invariant set in the setting of combinatorial and classical dynamical systems. We…

We say that a fixed point of a diffeomorphism is non-degenerate if 1 is not an eigenvalue of the linearization at the fixed point. We use pseudo-holomorphic curves techniques to prove the following: the inclusion map $$i: \text{Diff} ^{1}…

In this article we show that the braid type of a set of $1$-periodic orbits of a non-degenerate Hamiltonian diffeomorphism on a surface is stable under perturbations which are sufficiently small with respect to the Hofer metric $d_{\rm…

We call a symplectic rational surface $(X,\omega)$ \textit{positive} if $c_1(X)\cdot[\omega]>0$. The positivity condition of a rational surface is equivalent to the existence of a divisor $D\subset X$, such that $(X, D)$ is a log Calabi-Yau…

We develop sufficient analytic conditions for conservativeness of non-sectorial perturbations of symmetric Dirichlet forms which can be represented through a carr\'e du champ on a locally compact separable metric space. These form an…

The quantum theory of a massless spin two particle is strongly constrained by diffeomorphism invariance, which is in turn implied by unitarity. We explicitly exhibit the space-time diffeomorphism algebra of string theory, realizing it in…

The comparison principle for scalar second order parabolic PDEs on functions $u(t,x)$ admits a topological interpretation: pairs of solutions, $u^1(t,\cdot)$ and $u^2(t,\cdot)$, evolve so as to not increase the intersection number of their…