Homology surgery and invariants of 3-manifolds.
Homology theory for the set-theoretic Yang-Baxter equation and knot invariants from generalizations of quandles
A homology theory is developed for set-theoretic Yang-Baxter equations, and knot invariants are constructed by generalized colorings by biquandles and Yang-Baxter cocycles.
Homomorphic extensions of Johnson homomorphisms via Fox calculus
Using Fox differential calculus, for any positive integer , we construct a map on the mapping class group of a surface of genus with one boundary component, such that, when restricted to an appropriate subgroup, it coincides with the Johnson-Morita homomorphism. This allows us to construct very easily a homomorphic extension to of the second and third Johnson-Morita homomorphisms.
Homotopy and isotopy in dimension three.
Homotopy classification of nanophrases with at most four letters
We give a homotopy classification of nanophrases with at most four letters. It is an extension of the classification of nanophrases of length 2 with at most four letters, given by the author in a previous paper. As a corollary, we give a stable classification of ordered, pointed, oriented multi-component curves on surfaces with minimal crossing number less than or equal to 2 such that any equivalent curve has no simply closed curves in its components.
Homotopy dimension and simple cohomological dimension of spaces.
Homotopy groups of arc complements in or Q
Homotopy invariance of higher signatures and -manifold groups
For closed oriented manifolds, we establish oriented homotopy invariance of higher signatures that come from the fundamental group of a large class of orientable -manifolds, including the “piecewise geometric” ones in the sense of Thurston. In particular, this class, that will be carefully described, is the class of all orientable -manifolds if the Thurston Geometrization Conjecture is true. In fact, for this type of groups, we show that the Baum-Connes Conjecture With Coefficients holds. The...
Homotopy invariants of links.
Homotopy Lie algebras and fundamental groups via deformation theory
We formulate first results of our larger project based on first fixing some easily accessible invariants of topological spaces (typically the cup product structure in low dimensions) and then studying the variations of more complex invariants such as (the homotopy Lie algebra) or (the graded Lie algebra associated to the lower central series of the fundamental group). We prove basic rigidity results and give also an application in low-dimensional topology.
Homotopy Lie algebras; lower central series and the Koszul property.
Hopf diagrams and quantum invariants.
Hyperbolic cone-manifolds with large cone-angles.
Hyperbolic covering knots.
Hyperbolic groups with low-dimensional boundary
Hyperbolic knots and cyclic branched covers.
We collect several results on the determination of hyperbolic knots by means of their cyclic branched covers. We construct examples of knots having two common cyclic branched covers. Finally, we briefiy discuss the problem of determination of hyperbolic links.
Hyperbolic structure on a complement of tori in the 4-sphere.
Hyperbolic volume and mod p homology.