Related papers: Finite type invariants of 3-manifolds

The main result of this paper was already obtained in the paper `Some Remarks on the Geometry of Austere Manifolds', by Robert L. Bryant.

This is the first in a series of papers where we will derive invariants of three-manifolds and framed knots in them from the geometry of a manifold pseudotriangulation put in some way in a four-dimensional Euclidean space. Thus, the…

The paper is a survey of known periodicity properties of finite type invariants of knots, and their applications.

We explicitly construct small triangulations for a number of well-known 3-dimensional manifolds and give a brief outline of some aspects of the underlying theory of 3-manifolds and its historical development.

We prove:(1) the existence, for every integer n > 3, of a noncompact smooth n-dimensional topological manifold whose diffeomorphism group contains an isomorphic copy of every finitely presented group; (2) a finiteness theorem on finite…

A clover is a framed trivalent graph with some additional structure, embedded in a 3-manifold. We define surgery on clovers, generalizing surgery on Y-graphs used earlier by the second author to define a new theory of finite-type invariants…

Updated rerefences and introduction. Given a knot in an integer homology sphere, one can construct a family of closed 3-manifolds (parametrized by the positive integers), namely the cyclic branched coverings of the knot. In this paper we…

We introduce an (equi-)affine invariant diffusion geometry by which surfaces that go through squeeze and shear transformations can still be properly analyzed. The definition of an affine invariant metric enables us to construct an invariant…

In this paper, we study modular transformation properties of a certain class of functions with indefinite quadratic forms.

A brief exposition of the point of higher topos theory in (mathematical) physics, commissioned for the Encyclopedia of Mathematical Physics 2nd ed.

Draft version of an article prepared for the Encyclopedia of Mathematical Physics, Elsevier, to appear in 2006.

A version of Kirby calculus for spin and framed three-manifolds is given and is used to construct invariants of spin and framed three-manifolds in two situations. The first is ribbon *-categories which possess odd degenerate objects. This…

A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the…

Analogue of Springer's formula for the Poincar\'e series of the algebra invariants of ternary form is found.

One method for obtaining every closed orientable 3-manifold is as branched covering of the 3-sphere over a link. There is a classical topological result showing that the minimun possible number of sheets in the covering is three. In this…

Using the method of moving frames we analyze the algebra of differential invariants for surfaces in three-dimensional affine geometry. For elliptic, hyperbolic, and parabolic points, we show that if the algebra of differential invariants is…

In this paper we give a survey of elliptic theory for operators associated with diffeomorphisms of smooth manifolds. Such operators appear naturally in analysis, geometry and mathematical physics. We survey classical results as well as…

We give a survey of the theory of finite quantum groupoids (weak Hopf algebras), including foundations of the theory and applications to finite depth subfactors, dynamical deformations of quantum groups, and invariants of knots and…

In this article, we consider surfaces in the 3-dimensional Euclidean space E3 without parabolic points which are of finite II-type, that is, they are of finite type, in the sense of B.-Y. Chen, corresponding to the second fundamental form.…

Short review article on quantum computation accepted for Supplement III, Encyclopaedia of Mathematics (publication expected Summer 2001). See also http://www.wkap.nl/series.htm/ENM