Related papers: Finite type invariants of 3-manifolds

This is an overview article on finite type invariants, written for the Encyclopedia of Mathematical Physics

A theory of finite type invariants for arbitrary compact oriented 3-manifolds is proposed, and illustrated through many examples arising from both classical and quantum topology. The theory is seen to be highly non-trivial even for…

In this paper we develop the theory of finite-type invariants for homologically nontrivial 3-manifolds. We construct an infinite-dimensional affine space with a hypersurface in it corresponding to manifolds with Morse singularities.…

In this paper give a survey about L^2-invariants focusing on 3-manifolds.

This is a revised version (replacing an older one) with typos fixed and the introduction expanded.

We construct a hyperbolic three-manifold with trivial finite type invariants up to a given degree.

A new class of 3-manifold invariants is constructed from representations of the category of framed tangles.

This is a latest survey article on embeddings of multibranched surfaces into 3-manifolds.

This article surveys invariants of four-manifolds and their relation to Donaldson-Witten theory, and other topologically twisted Yang-Mills theories. The article is written for the second edition of the Encyclopedia of Mathematical Physics,…

Submanifolds of finite type were introduced by the author during the late 1970s. The first results on this subject had been collected in author's book [Total mean curvature and sub manifolds of finite type, World Scientific, NJ, 1984]. A…

This is an expository article for Elsevier's Encyclopedia of Mathematical Physics on the subject in the title. Comments/corrections welcome.

This paper studies invariants of 3-manifolds derived from certain fin ite dimensional Hopf algebras. The invariants are based on right integrals for these algebras. It is shown that the resulting class of invariants is distinct from the…

This paper is devoted to a discussion of specific properties of invariants in the theory of forms.

We introduce the notion of weight system for finite type invariants of integral homology 3-spheres, and we show that invariants of type m are determined, modulo invariants of type m-1, by their associated weight system.

To appear in Encyclopedia of Mathematical Physics, published by Elsevier in early 2006. Comments/corrections welcome. The article surveys topological aspects in gauge theories.

The aim of this work is to offer a family of invariants that allows us to classify finite potent endomorphisms on arbitrary vector spaces, generalizing the classification of endomorphisms on finite-dimensional vector spaces. As a particular…

In this paper we develop a theory for constructing an invariant of closed oriented 3-manifolds, given a certain type of Hopf algebra. Examples are given by a quantised enveloping algebra of a semisimple Lie algebra, or by a semisimple…

An expository survey article on Heegaard splittings

This is an overview article on finite-dimensional algebras and quivers, written for the Encyclopedia of Mathematical Physics. We cover path algebras, Ringel-Hall algebras and the quiver varieties of Lusztig and Nakajima.

This study defines finite-type invariants for curves on surfaces and reveals the construction of these finite-type invariants for stable homeomorphism classes of curves on compact oriented surfaces without boundaries. These invariants are a…