Abstract The Geometric Shafarevich Conjecture and the Theorem of de Franchis state finiteness number certain holomorphic objects on closed or punctured Riemann surfaces. analog these kind theorems for surfaces second is an estimate irreducible up to homotopy (or isotopy, respectively). This can be interpreted as a quantitatve statement limitation Gromov’s Oka principle. For any finite open surf...

In [12] is established that knot isotopy in a 3-manifold may be interpreted in terms of Markov braid equivalence and, also, that the braids related to the 3-manifold form algebraic structures. Moreover, the sets of braids related to the solid torus or to the lens spaces L(p, 1) form groups, which are in fact the Artin braid groups of type B. As a consequence, in [12, 13] appeared the first cons...

We construct an enhanced version of knot contact homology, and show that we can deduce from it the group ring of the knot group together with the peripheral subgroup. In particular, it completely determines a knot up to smooth isotopy. The enhancement consists of the (fully noncommutative) Legendrian contact homology associated to the union of the conormal torus of the knot and a disjoint cotan...

Let B be a 3-dimensional handlebody of genus g. Let M be the group of the isotopy classes of orientation preserving homeomorphisms of B. We construct a 2-dimensional simplicial complex X, connected and simply-connected, on which M acts by simplicial transformations and has only a finite number of orbits. From this action we derive an explicit finite presentation ofM. We consider a 3-dimensional...

This paper uses an elementary surgery technique to give a simple topological proof of a theorem of Harer which says that the simplicial complex having as its top-dimensional simplices the isotopy classes of triangulations of a compact surface with a fixed set of vertices is contractible, except in a few special cases when it is homeomorphic to a sphere. (Triangulations here are allowed to have ...

We extend the characterization of virtual permutation endomorphisms in the case where IIi(Ai) = Zn. We show that for endomorphisms of Z[Zn] complexes the appropriate eigenvalue condition is that all eigenvalues be roots of units of the group ring Z[Zn\. Among these endomorphisms the virtual permutations are detected by Kq. The main application is in identifying Morse-Smale isotopy classes on th...

This is the third of three papers about the Compression Theorem: if M m is embedded in Q q R with a normal vector eld and if q ? m 1, then the given vector eld can be straightened (ie, made parallel to the given R direction) by an isotopy of M and normal eld in Q R. The theorem can be deduced from Gromov's theorem on directed em-beddings 3; 2.4.5 (C 0)] and the rst two parts gave proofs. Here w...

We show that for given four points in the Riemann sphere and a isotopy class of two disjoint arcs connecting these pairs, there exists unique configuration with property each arc is hyperbolic geodesic segment complement other arc.