Integral HOMFLY-PT and -link homology.
Integral lattices in TQFT
Intersections in hyperbolic manifolds.
Intrinsic knotting and linking of complete graphs.
Intrinsic linking and knotting are arbitrarily complex
We show that, given any n and α, any embedding of any sufficiently large complete graph in ℝ³ contains an oriented link with components Q₁, ..., Qₙ such that for every i ≠ j, and , where denotes the second coefficient of the Conway polynomial of .
Intrinsically linked graphs and even linking number.
Introducing Regina, the 3-manifold topology software.
Introduction to the basics of Heegaard Floer homology
This paper provides an introduction to the basics of Heegaard Floer homology with some emphasis on the hat theory and to the contact geometric invariants in the theory. The exposition is designed to be comprehensible to people without any prior knowledge of the subject.
Invariantes topológicos en el ADN, los Fullerenos y la Teoría de Elección Social.
Invariants de Vassiliev des nœuds
Invariants from triangulations of hyperbolic 3-manifolds.
Invariants of 3-manifolds via link polynomials and quantum groups.
Invariants of -type links via an extension of the Kauffman bracket.
Invariants of branched covering from the work of Serre and Mumford.
Invariants of piecewise-linear knots
We study numerical and polynomial invariants of piecewise-linear knots, with the goal of better understanding the space of all knots and links. For knots with small numbers of edges we are able to find limits on polynomial or Vassiliev invariants sufficient to determine an exact list of realizable knots. We thus obtain the minimal edge number for all knots with six or fewer crossings. For example, the only knot requiring exactly seven edges is the figure-8 knot.
Invertible Amphicheiral Knots.
Involutions in mapping class groups of non-orientable surfaces.
We prove that the mapping class group and the pure mapping class group of closed non-orientable surfaces with punctures are generated by involutions.
Involutions of 3-dimensional handlebodies
We study the orientation preserving involutions of the orientable 3-dimensional handlebody , for any genus g. A complete classification of such involutions is given in terms of their fixed points.
Involutory Hopf group-coalgebras and flat bundles over 3-manifolds
Given a group π, we use involutory Hopf π-coalgebras to define a scalar invariant of flat π-bundles over 3-manifolds. When π = 1, this invariant equals the one for 3-manifolds constructed by Kuperberg from involutory Hopf algebras. We give examples which show that this invariant is non-trivial.
Involving symmetries of Riemann surfaces to a study of the mapping class group.