Algebraic Geometry

Download A Survey of Knot Theory by Akio Kawauchi PDF

By Akio Kawauchi

Knot conception is a swiftly constructing box of analysis with many functions not just for arithmetic. the current quantity, written via a widely known expert, provides a whole survey of knot concept from its very beginnings to state-of-the-art newest examine effects. the subjects contain Alexander polynomials, Jones sort polynomials, and Vassiliev invariants. With its appendix containing many beneficial tables and a longer record of references with over 3,500 entries it really is an essential e-book for everybody desirous about knot concept. The publication can function an creation to the sector for complicated undergraduate and graduate scholars. additionally researchers operating in open air components reminiscent of theoretical physics or molecular biology will make the most of this thorough research that is complemented by way of many workouts and examples.

Show description

Read or Download A Survey of Knot Theory PDF

Similar algebraic geometry books

A basic course in algebraic topology

This publication is meant to function a textbook for a direction in algebraic topology at first graduate point. the most subject matters lined are the class of compact 2-manifolds, the elemental staff, protecting areas, singular homology thought, and singular cohomology conception. those issues are built systematically, keeping off all unecessary definitions, terminology, and technical equipment.

Algebra in the Stone-Cech Compactification: Theory and Applications (De Gruyter Expositions in Mathematics, 27)

This paintings provides a research of the algebraic homes of compact correct topological semigroups commonly and the Stone-Cech compactification of a discrete semigroup specifically. a number of robust purposes to combinatorics, basically to the department of combinarotics often called Ramsey concept, are given, and connections with topological dynamics and ergodic thought are offered.

Complex Analysis in One Variable

This ebook offers advanced research in a single variable within the context of contemporary arithmetic, with transparent connections to a number of advanced variables, de Rham concept, actual research, and different branches of arithmetic. therefore, protecting areas are used explicitly in facing Cauchy's theorem, actual variable tools are illustrated within the Loman-Menchoff theorem and within the corona theorem, and the algebraic constitution of the hoop of holomorphic services is studied.

Sasakian Geometry

This publication is an in depth monograph on Sasakian manifolds, targeting the complicated dating among okay er and Sasakian geometries. the topic is brought by means of dialogue of numerous heritage themes, together with the idea of Riemannian foliations, compact complicated and okay er orbifolds, and the life and obstruction concept of okay er-Einstein metrics on advanced compact orbifolds.

Additional resources for A Survey of Knot Theory

Example text

2) If L1~L2 is a trivial knot, then L1 and L2 are trivial knots. (1) is directly proved by a cut-and-paste argument of combinatorial topology. (2) is usually obtained from Schubert's result on the additivity of the knot genus (cf. , g(Ll~L2) = geLd + g(L2) (which is also proved by a cut-and-paste argument). 2 A link L is locally trivial if any 2-sphere S in S3 which intersects L transversally in two points bounds a 3-ball intersecting L in a trivial arc. 3 Show the following statements: (1) A trivial knot is locally trivial.

3) A non-trivial torus knot is not amphicheiral. 15. 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.

Further, prove that this presentation is unique up to the relation D(b 1 , b2 , . ,bn ) = D(-b n , ... , -b 2 , -b 1 ). < . ~ >c'< . x: 2~ 2~ " 2h, C :x :~: (n is odd) :X . )2 ] 2b, (n is even) Fig. 15. If we reverse the orientation of one of the two components of 5(4,1) = D( -1,1, -1), then we obtain 5(4, -3) = D(2). 16 Prove that there exists an ambient isotopy of 53 which interchanges the components of a 2-component 2-bridge link so that the link orientation remains as it was. 2 Torus links A torus link is a link embedded in the standard torus T in 53.

Download PDF sample

Rated 4.18 of 5 – based on 32 votes