For a homeomorphism $T \colon X \to X$ of Cantor set $X$, the mapping class group $\mathcal {M}(T)$ is isotopy classes orientation-preserving self-homeomorphisms suspension $\Sigma _{T}X$. The can be interp

2 2 Abstract. We consider a locally flat 2-sphere in S x S representing a primi2 2 tive homology class £ , which is referred to as a 2-knot in S x S representing 2 2 (J . Then for any given primitive class ¿ , there exists a 2-knot in S x S representing { with simply-connected complement. In this paper, we consider the 2 2 classification of 2-knots in S x S whose complements have a fixed fundam...

Studying the space of Lagrangian submanifolds is a fundamental problem in symplectic topology. Lagrangian spheres appear naturally in the Leftschetz pencil picture of symplectic manifolds. In this paper we demonstrate the uniqueness up to Hamiltonian isotopy of the Lagrangian spheres in some 4-dimensional Stein symplectic manifolds. The most important example is the cotangent bundle of the 2-sp...

In the past few years there have been several striking results about the topology of Lagrangian surfaces in symplectic four-manifolds. The general tendency of these results is that many isotopy classes of embedded surfaces do not contain Lagrangian representatives. This is called the topological unknottedness of Lagrangian surfaces; see [4] for a survey. The aim of this paper is to complement t...

In the theory of surface diffeomorphisms relative to homoclinic and heteroclinic orbits, it is possible to compute a one-dimensional representative map for any irreducible isotopy class. The topological entropy of this graph representative is equal to the growth rate of the number of essential Nielsen classes of a given period, and hence is a lower bound for the topological entropy of the diffe...