By Kunio Murasugi
Knot idea is an idea in algebraic topology that has came across functions to quite a few mathematical difficulties in addition to to difficulties in computing device technology, organic and clinical learn, and mathematical physics. This e-book is directed to a wide viewers of researchers, starting graduate scholars, and senior undergraduate scholars in those fields.
The ebook comprises lots of the basic classical proof concerning the conception, similar to knot diagrams, braid representations, Seifert surfaces, tangles, and Alexander polynomials; additionally integrated are key more moderen advancements and particular subject matters equivalent to chord diagrams and overlaying areas. The paintings introduces the attention-grabbing examine of knots and offers perception into purposes to such reviews as DNA learn and graph thought. moreover, each one bankruptcy encompasses a complement that comprises attention-grabbing old in addition to mathematical comments.
The writer essentially outlines what's recognized and what's now not identified approximately knots. He has been cautious to prevent complicated mathematical terminology or complicated innovations in algebraic topology or workforce conception. there are lots of diagrams and workouts bearing on the cloth. The learn of Jones polynomials and the Vassiliev invariants are heavily examined.
"The e-book ...develops knot concept from an intuitive geometric-combinatorial perspective, keeping off thoroughly extra complex techniques and methods from algebraic topology...Thus the emphasis is on a lucid and intuitive exposition available to a broader audience... The booklet, written in a stimulating and unique variety, will function a primary method of this attention-grabbing box for readers with a number of backgrounds in arithmetic, physics, and so forth. it's the first textual content constructing contemporary subject matters because the Jones polynomial and Vassiliev invariants on a degree available additionally for non-specialists within the field." -Zentralblatt Math