Heegaard Splittings and Branched Coverings of B3.
Heegaard splittings and virtually Haken Dehn filling.
Heegaard splittings of exteriors of two bridge knots.
Heegaard splittings of the pair of solid torus and the core loop.
We show that any Heegaard splitting of the pair of the solid torus (≅D2xS1) and its core loop (an interior point xS1) is standard, using the notion of Heegaard splittings of pairs of 3-manifolds and properly imbedded graphs, which is defined in this paper.
Hodge–type structures as link invariants
Based on some analogies with the Hodge theory of isolated hypersurface singularities, we define Hodge–type numerical invariants of any, not necessarily algebraic, link in a three–sphere. We call them H–numbers. They contain the same amount of information as the (non degenerate part of the) real Seifert matrix. We study their basic properties, and we express the Tristram–Levine signatures and the higher order Alexander polynomial in terms of them. Motivated by singularity theory, we also introduce...
Homfly polynomials as vassiliev link invariants
We prove that the number of linearly independent Vassiliev invariants for an r-component link of order n, which derived from the HOMFLY polynomial, is greater than or equal to min{n,[(n+r-1)/2]}.
Homfly polynomials of generalized Hopf links.
Homogeneously wild curves and infinite knot products
Homological Identities for Closed Orbits.
Homology 3-Spheres which are Obtained by Dehn Surgeries on Knots.
Homology cylinders: an enlargement of the mapping class group.
Homology lens spaces and Dehn surgery on homology spheres
A homology lens space is a closed 3-manifold with ℤ-homology groups isomorphic to those of a lens space. A useful theorem found in [Fu] states that a homology lens space may be obtained by an (n/1)-Dehn surgery on a homology 3-sphere if and only if the linking form of is equivalent to (1/n). In this note we generalize this result to cover all homology lens spaces, and in the process offer an alternative proof based on classical 3-manifold techniques.
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.
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 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.
Hyperbolic covering knots.
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.