A Survey of Knot Theory by Akio Kawauchi

By Akio Kawauchi

Knot thought is a speedily constructing box of analysis with many functions, not just for arithmetic. the current quantity, written by means of a well known professional, offers a whole survey of this idea from its very beginnings to present day most up-to-date study effects. An integral e-book for everybody keen on knot theory.

Show description

Read or Download A Survey of Knot Theory PDF

Best algebraic geometry books

Hodge theory and complex algebraic geometry 1

This can be a smooth advent to Kaehlerian geometry and Hodge constitution. assurance starts off with variables, complicated manifolds, holomorphic vector bundles, sheaves and cohomology conception (with the latter being handled in a extra theoretical means than is common in geometry). The booklet culminates with the Hodge decomposition theorem.

Logarithmic Forms and Diophantine Geometry

There's now a lot interaction among reports on logarithmic kinds and deep features of mathematics algebraic geometry. New mild has been shed, for example, at the recognized conjectures of Tate and Shafarevich on the subject of abelian kinds and the linked celebrated discoveries of Faltings constructing the Mordell conjecture.

Geometry of Higher Dimensional Algebraic Varieties (Oberwolfach Seminars)

The topic of this e-book is the class idea and geometry of upper dimensional kinds: life and geometry of rational curves through attribute p-methods, manifolds with unfavorable Kodaira size, vanishing theorems, conception of extremal rays (Mori theory), and minimum types. The ebook provides a cutting-edge intro- duction to a tricky and never without problems available topic which has gone through huge, immense improvement within the final 20 years.

A Survey of Knot Theory

Knot idea is a swiftly constructing box of study with many purposes, not just for arithmetic. the current quantity, written by way of a well known expert, offers a whole survey of this concept from its very beginnings to modern-day newest learn effects. An critical ebook for everybody fascinated with knot thought.

Additional resources for A Survey of Knot Theory

Example text

15 Let Si and Sk be two Seifert circles in the system of Seifert circles of a link diagram D. Assume that Sk is outside Si and Si is outside Sk and their orientations are coherent. 16. Then we deform D by Reidemeister moves as follows: At first, stretch out Sk n b along b until CHAPTER 1 PRESENTATIONS 16 it is near Si. 18. This deformation of the system of Seifert circles is called a concentric deformation of type II. If we consider the system of Seifert circles on the sphere, the concentric deformation of type II is nothing but the concentric deformation of type I.

3 Establish a similar classification for torus links. 4 Find all of the torus links with crossing number S 10. 3 Pretzel links For non-zero integers ql, q2, ... 1 is called the pretzel link and denoted by P(ql, q2, ... , qm), where qi indicates Iqil crossing points with sign E = qi/lqil = ±1. Suppose that (q~, q&, ... , q~) is a cyclic permutation of (ql, q2, ... , qm). Then P(q~, q&, ... , q~) and P(ql, q2, ... , qm) are positive-equivalent. If qi = ±1, then P(ql, ... , qi, ... , qrn) is positive-equivalent to P(qi, ql, ...

7) of any pretzel link is a reflection group in 2-dimensional spherical, Euclidean or hyperbolic space, which has been known since the appearance of [Reidemeister 1932]. Chapter 3 Compositions and decompositions In this chapter, we discuss how to construct a new link from given links by various compositions. Then we discuss decompositions, which are the inverse operations of compositions. After that, compositions of tangles are discussed. Throughout this chapter, links are understood to be links in 83.

Download PDF sample

Rated 4.52 of 5 – based on 3 votes