Read e-book online A Survey of Knot Theory PDF

By Akio Kawauchi

ISBN-10: 3034892276

ISBN-13: 9783034892278

ISBN-10: 303489953X

ISBN-13: 9783034899536

Knot idea is a swiftly constructing box of study with many functions not just for arithmetic. the current quantity, written by means of a widely known professional, offers an entire survey of knot conception from its very beginnings to brand new latest learn effects. the themes contain Alexander polynomials, Jones kind polynomials, and Vassiliev invariants. With its appendix containing many beneficial tables and a longer checklist of references with over 3,500 entries it really is an necessary publication for everybody thinking about knot conception. The ebook can function an advent to the sector for complicated undergraduate and graduate scholars. additionally researchers operating in outdoor parts akin to theoretical physics or molecular biology will make the most of this thorough examine that is complemented by means of many routines and examples.

Show description

Read Online or Download A Survey of Knot Theory PDF

Similar algebraic geometry books

Get Complex Geometry PDF

Provides the lawsuits of a world convention on complicated geometry and similar issues, held in commemoration of the fiftieth anniversary of Osaka college, Osaka, Japan. The textual content makes a speciality of the CR invariants, hyperbolic geometry, Yamabe-type difficulties, and harmonic maps.

Explicit Birational Geometry of 3-folds by Corti A., Reid M. (eds.) PDF

One of many major achievements of algebraic geometry over the last 20 years is the paintings of Mori and others extending minimum versions and the Enriques-Kodaira type to 3-folds. This built-in suite of papers facilities round functions of Mori conception to birational geometry. 4 of the papers (those through Pukhlikov, Fletcher, Corti, and the lengthy joint paper via Corti, Pukhlikov and Reid) figure out intimately the idea of birational tension of Fano 3-folds.

Download PDF by Jean-Paul Brasselet, Jose Luis Cisneros-molina, David: Singularities I: Algebraic and Analytic Aspects:

This can be the 1st a part of the lawsuits of the assembly 'School and Workshop at the Geometry and Topology of Singularities', held in Cuernavaca, Mexico, from January eighth to twenty sixth of 2007, in social gathering of the sixtieth Birthday of Le Dung Trang. This quantity includes fourteen state-of-the-art study articles on algebraic and analytic features of singularities of areas and maps.

Additional resources for A Survey of Knot Theory

Sample text

1b is both atoroidal and anannular. 4 Show that a 2-string tangle is anannular if it is locally trivial and atoroidal. 5 A tangle (B, t) is hyperbolic if it is prime, atoroidal and anannular. 6 A link obtained from two hyperbolic tangles by any tangle sum is hyperbolic. 6. 7 Non-triviality of a link In this section, we discuss some results due to Y. Nakanishi on the non-triviality of a link containing a given tangle. 1 For a non-trivial 2-string tangle (E, t) and two 2-string tangles (A 1,81) and (A 2,82), we assume that the tangle sums (E, t) U

Fig. 8. 3 are prime tangles. 8. 10 For any n-string tangle, show that indivisibility implies local triviality. 11 For any n-string tangle with n ~ 2 except the trivial 2-string tangle, show that indivisibility implies primeness. 12 A link obtained from two prime tangles by any tangle sum is prime. The proof is in [Nakanishi 1981']. 4 are prime. 6. 14 Let (C, v) be a tangle and D be a disk properly embedded in C such that D divides (C,v) into two tangles (A,s) and (B,t). We assume the following: (1) The numbers of points in (8A - D) nv, (8B - D) nv and Dnv are all greater than or equal to two.

The following theorem means that the converse of this Proposition holds in part. 8 If two knot diagrams are R-isotopic and have the same twisting number, then they are regularly isotopic. - I. ~ I. * Fig. 7 JL Proof. 7. Obviously, the moves of type I:t- and type I~ are generated by the moves of type IV, type 1+ or type L. Therefore any R-isotopic diagrams can be transformed into each other by a finite sequence of the Reidemeister moves of type 1+, type L, type II, type III or type IV. Then we can postpone the Reidemeister moves of type 1+ and type L until the end of the sequence, although after this change, the length of the sequence may be longer than the original sequence.

Download PDF sample

A Survey of Knot Theory by Akio Kawauchi

by Jeff

Rated 4.40 of 5 – based on 26 votes