On branched coverings of 3-manifolds which fiber over the circle.
On Branched Coverings of the 3-Sphere.
On Cartesian powers of 2-polyhedra
On c-continuous fundamental groups
On Certain Permuation Representations of Mapping Class Groups.
On Chern-Simons invariants of geometric 3-manifolds.
On chirality groups and regular coverings of regular oriented hypermaps
We prove that if the Walsh bipartite map of a regular oriented hypermap is also orientably regular then both and have the same chirality group, the covering core of (the smallest regular map covering ) is the Walsh bipartite map of the covering core of and the closure cover of (the greatest regular map covered by ) is the Walsh bipartite map of the closure cover of . We apply these results to the family of toroidal chiral hypermaps induced by the family of toroidal bipartite maps...
On closed subgroups of the group of homeomorphisms of a manifold
Let be a triangulable compact manifold. We prove that, among closed subgroups of (the identity component of the group of homeomorphisms of ), the subgroup consisting of volume preserving elements is maximal.
On constructions of generalized skein modules
Józef Przytycki introduced skein modules of 3-manifolds and skein deformation initiating algebraic topology based on knots. We discuss the generalized skein modules of Walker, defined by fields and local relations. Some results by Przytycki are proven in a more general setting of fields defined by decorated cell-complexes in manifolds. A construction of skein theory from embedded TQFT-functors is given, and the corresponding background is developed. The possible coloring of fields by elements of...
On contractible open 3-manifolds.
On Culler-Shalen seminorms and Dehn filling.
On Cyclic Branched Coverings of Spheres.
On decomposition of 3-polyhedra into a Cartesian product
On deformations of hyperbolic 3-manifolds with geodesic boundary.
On diffeomorphisms over surfaces trivially embedded in the 4-sphere.
On Dihedral Covering Spaces of Knots.
On Embedded Spheres in 3-manifolds.
On equivariant deformations of maps.
We work in the smooth category: manifolds and maps are meant to be smooth. Let G be a finite group acting on a connected closed manifold X and f an equivariant self-map on X with f|A fixpointfree, where A is a closed invariant submanifold of X with codim A ≥ 3. The purpose of this paper is to give a proof using obstruction theory of the following fact: If X is simply connected and the action of G on X - A is free, then f is equivariantly deformable rel. A to fixed point free map if and only if the...
On finite groups acting on a connected sum of 3-manifolds S² × S¹
Let denote the closed 3-manifold obtained as the connected sum of g copies of S² × S¹, with free fundamental group of rank g. We prove that, for a finite group G acting on which induces a faithful action on the fundamental group, there is an upper bound for the order of G which is quadratic in g, but there does not exist a linear bound in g. This implies then a Jordan-type bound for arbitrary finite group actions on which is quadratic in g. For the proofs we develop a calculus for finite group...
On finite groups acting on acyclic low-dimensional manifolds
We consider finite groups which admit a faithful, smooth action on an acyclic manifold of dimension three, four or five (e.g. Euclidean space). Our first main result states that a finite group acting on an acyclic 3- or 4-manifold is isomorphic to a subgroup of the orthogonal group O(3) or O(4), respectively. The analogous statement remains open in dimension five (where it is not true for arbitrary continuous actions, however). We prove that the only finite nonabelian simple groups admitting a smooth...