By J. Scott Carter

During this booklet the authors enhance the speculation of knotted surfaces in analogy with the classical case of knotted curves in three-d house. within the first bankruptcy knotted floor diagrams are outlined and exemplified; those are customary surfaces in 3-space with crossing info given. The diagrams are extra greater to offer substitute descriptions. A knotted floor may be defined as a film, as a type of categorised planar graph, or as a chain of phrases within which successive phrases are similar via grammatical adjustments. within the moment bankruptcy, the idea of Reidemeister strikes is constructed within the numerous contexts. The authors convey the way to unknot tricky examples utilizing those strikes. The 3rd bankruptcy stories the braid idea of knotted surfaces. Examples of the Alexander isotopy are given, and the braid motion picture strikes are awarded. within the fourth bankruptcy, homes of the projections of knotted surfaces are studied. orientated surfaces in 4-space are proven to have planar projections with no cusps and with out department issues. indicators of triple issues are studied. functions of triple-point smoothing that come with proofs of triple-point formulation and an explanation of Whitney's congruence on basic Euler periods are offered. The 5th bankruptcy exhibits easy methods to receive shows for the elemental crew and the Alexander modules. Key examples are labored intimately. The Seifert set of rules for knotted surfaces is gifted and exemplified. The 6th bankruptcy relates knotted surfaces and diagrammatic recommendations to 2-categories. ideas to the Zamolodchikov equations which are diagrammatically received are offered. The booklet includes over 2 hundred illustrations that light up the textual content. Examples are labored out intimately, and readers find a way to profit first-hand a chain of outstanding geometric innovations.

Show description

Read or Download Knotted Surfaces and Their Diagrams (Mathematical Surveys and Monographs) PDF

Best Algebraic Geometry books

An Introduction to Algebraic Geometry and Algebraic Groups (Oxford Graduate Texts in Mathematics)

An available textual content introducing algebraic geometries and algebraic teams at complex undergraduate and early graduate point, this booklet develops the language of algebraic geometry from scratch and makes use of it to establish the idea of affine algebraic teams from first ideas. construction at the history fabric from algebraic geometry and algebraic teams, the textual content offers an creation to extra complex and specialized fabric.

The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics)

The idea of elliptic curves is exotic through its lengthy background and via the variety of the equipment which have been utilized in its research. This booklet treats the mathematics method in its sleek formula, by using uncomplicated algebraic quantity concept and algebraic geometry. Following a quick dialogue of the required algebro-geometric effects, the ebook proceeds with an exposition of the geometry and the formal crew of elliptic curves, elliptic curves over finite fields, the complicated numbers, neighborhood fields, and worldwide fields.

Foundations of Hyperbolic Manifolds (Graduate Texts in Mathematics)

This seriously class-tested booklet is an exposition of the theoretical foundations of hyperbolic manifolds. it's a either a textbook and a reference. A uncomplicated wisdom of algebra and topology on the first yr graduate point of an American college is thought. the 1st half is anxious with hyperbolic geometry and discrete teams.

Additional info for Knotted Surfaces and Their Diagrams (Mathematical Surveys and Monographs)

Show sample text content

Rated 4.20 of 5 – based on 30 votes