相关论文: Finite Type Invariants

We estabilish some connections among the Makar-Limanov invariant, the Derksen invariant, and the existence of flexible points on an affine variety.

We give a complete description of all order 1 invariants of planar curves.

Submanifolds of finite type were introduced by the author during the late 1970s. The first results on this subject were collected in author's books [26,29]. In 1991, a list of twelve open problems and three conjectures on finite type…

In the finite dimensional case, mean-type mappings, their invariant means, relations between the uniqueness of invariant means and convergence of orbits of the mapping, are considered. In particular it is shown, that the uniqueness of an…

This is a concise overview of the definitions and properties of the linking number and its higher-order generalization, Milnor invariants.

A. Henrich proved the existence of the universal finite-type invariant of order one for virtual knots. We extend the construction and the methods of her paper to framed virtual knots. To do so, we introduce the notions of virtual strings…

We survey new results on finite groups of birational transformations of algebraic varieties.

We introduce subshifts of quasi-finite type as a generalization of the well-known subshifts of finite type. This generalization is much less rigid and therefore contains the symbolic dynamics of many non-uniform systems, e.g., piecewise…

This brief note, written for non-specialists, aims at drawing an introductive overview of the multiverse issue.

This is a brief overview of a few selected chapters on automorphism groups of affine varieties. It includes some open questions.

This is a survey of known algorithms in algebraic topology with a focus on finite simplicial complexes and, in particular, simplicial manifolds. Wherever possible an elementary approach is chosen. This way the text may also serve as a…

In this paper, we discuss the birational invariance of the class of balanced hyperbolic manifolds.

A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. The associated special functions are eigenfunctions of some shape invariant operators. These operators can…

This paper discusses some topics of enquiry concerning fractals, functions on them, and so on.

A brief introduction to exterior differential systems for graduate students familiar with manifolds and differential forms. For complete files, see https://github.com/Ben-McKay/introduction-to-exterior-differential-systems

This is a short survey on finite-volume hyperbolic four-manifolds. We describe some general theorems and focus on the concrete examples that we found in the literature. The paper contains no new result.

A review of the inverse scattering transform is given, and an introduction to solitons is provided.

This is a survey article to be part of the Encyclopedia of Mathematical Physics, to be published by Elsevier in the beginning of 2006.

Several examples are used to illustrate how we deal cavalierly with infinities and unphysical systems in physics. Upon examining these examples in the context of infinities from Cantor's theory of transfinite numbers, the only known…

A concise introduction to the Standard Model of fundamental particle interactions is presented.