Löbell manifolds revised.
Local coordinates for -character varieties of finite-volume hyperbolic 3-manifolds
Given a finite-volume hyperbolic 3-manifold, we compose a lift of the holonomy in with the -dimensional irreducible representation of in . In this paper we give local coordinates of the -character variety around the character of this representation. As a corollary, this representation is isolated among all representations that are unipotent at the cusps.
Local rigidity of aspherical three-manifolds
In this paper we construct, for each aspherical oriented -manifold , a -dimensional class in the -homology of whose norm combined with the Gromov simplicial volume of gives a characterization of those nonzero degree maps from to which are homotopic to a covering map. As an application we characterize those degree one maps which are homotopic to a homeomorphism in term of isometries between the bounded cohomology groups of and .
Localization of group rings and applications to 2-complexes.
Locally unknotted spines of Heegaard splittings.
Longitude Floer homology and the Whitehead double.
L'ordre de Dehornoy sur les tresses
Malnormal subgroups and Frobenius groups: basics and examples
Malnormal subgroups occur in various contexts. We review a large number of examples, and compare the general situation to that of finite Frobenius groups of permutations.In a companion paper [18], we analyse when peripheral subgroups of knot groups and -manifold groups are malnormal.
Manifold structures on abstract regular polytopes.
Manifolds as branched covers of spheres.
Manifolds of even dimension with amenable fundamental group.
Manifolds with a given homology and fundamental gorup.
Mapping class group and the Casson invariant
Using a new definition of the second and third Johsnon homomorphisms, we simplify and extend the work of Morita on the Casson invariant of homology-spheres defined by Heegard splittings. In particular, we calculate the Casson invariant of the homology-sphere obtained by gluing two handlebodies along a homeomorphism of the boundary belonging to the Torelli subgroup.
Mapping class group of a handlebody
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 of ℳ.
Mapping tori of free group automorphisms are coherent.
Mappings of reducible 3-manifolds
Markov traces and knot invariants related to Iwahori-Hecke algebras of type B.
Mathematical properties of DNA structure in 3-dimensional space.
Matrix factorizations and link homology
For each positive integer n the HOMFLYPT polynomial of links specializes to a one-variable polynomial that can be recovered from the representation theory of quantum sl(n). For each such n we build a doubly-graded homology theory of links with this polynomial as the Euler characteristic. The core of our construction utilizes the theory of matrix factorizations, which provide a linear algebra description of maximal Cohen-Macaulay modules on isolated hypersurface singularities.
Maximal actions of finite 2-groups on ℤ₂-homology 3-spheres
It is known that a finite 2-group acting on a ℤ₂-homology 3-sphere has at most ten conjugacy classes of involutions; the action of groups with the maximal number of conjugacy classes of involutions is strictly related to some questions concerning the representation of hyperbolic 3-manifolds as 2-fold branched coverings of knots. Using a low-dimensional approach we classify these maximal actions both from an algebraic and from a geometrical point of view.