I took intro to knot theory as a 300 level course junior level. If both ends of the line will be loaded, then the clove hitch will. The paper is relatively selfcontained and it describes virtual knot theory both combinatorially and in terms of the knot theory in thickened surfaces. Interactive knot theory with knotplot springerlink. We describe the computer program knotplot, a topological drawing tool for knots and links. An interactive introduction to knot theory inga johnson. Read an interactive introduction to knot theory online by inga. She also coauthored the book a mathematicians practical guide to mentoring undergraduate research with michael dorff and lara pudwell, mathematical association of america, american mathematical society. You can hand in your solutions in the letter box in hg f 28. Introduction knot theory as we know it first gained prominence as a. Subsequent chapters guide the reader to discover the formal definition of a knot, families of knots and links, and various knot notations. This decomposition appears in thurstons notes 19, and with a. In my opinion it works well after calculus, linear algebra, andor differential equations, but technically does not require any knowledge on any of those subject matters.
Prerequisites are only a basic familiarity with linear algebra and a. This wellwritten and engaging volume, intended for. They can be admired as artifacts of the decorative arts and crafts, or viewed as accessible intimations. This paper is an introduction to virtual knot theory and an exposition of new ideas and constructions, including the parity bracket polynomial, the arrow polynomial, the parity arrow polynomial and categorifications of the arrow polynomial. For flat material such as seatbelts, the water knot is best. Introduction to knot theory chris john february, 2016 supervised by dr. We can visualize a mathematical knot as a knot that we would encounter in our everyday experience, but with the loose ends glued together. Some of the material will be used later in this report, while some is included simply to give an idea of di erent techniques used in knot theory. Dover modern math originals paperback january 18, 2017 by inga johnson author, allison k. Sections 6 and 7 provide an introduction to vassiliev invariants and the remarkable relationship between lie algebras and knot theory. An introduction to the theory of knots computer graphics. Jan 04, 2011 this paper is an introduction to virtual knot theory and an exposition of new ideas and constructions, including the parity bracket polynomial, the arrow polynomial, the parity arrow polynomial and categorifications of the arrow polynomial. Recall that a graph consists of a set of vertices and a set of edges that connect them.
I describe the homologies of covering spaces of a knot, the alexander polynomial, the homfly polynomial. An introduction to knot theory university of newcastle. Prerequisites are only a basic familiarity with linear algebra and a willingness to explore the subject in a handson manner. Spectacular graphics make this online game instructional and fun. Jump right into the action on the interactive search for a master of knot disguise. See all 2 formats and editions hide other formats and editions. A beginning for knot theory 1 exercises chapter 2. Use features like bookmarks, note taking and highlighting while reading an interactive introduction to knot theory aurora. Knots can be studied at many levels and from many points of view. Polyhedral decomposition of the figure8 knot complement 2. The fishermans knot is similar but easier to tie with cold, wet hands.
The ideas used in this chapter can be found in most introductory books or courses on. Interactive introduction to knot theory by allison k. A knot is any closed nonselfintersecting loop embedded in three dimensions. Seifert surfaces and knot factorisation 15 exercises 21 chapter 3. Our exploration of the history of knot theory will conclude with a discussion of current conjecture regarding possible applications and the direction of the future of knot theory. A framed knot is the extension of a tame knot to an embedding of the solid torus d 2. An interactive introduction to knot theory an interactive introduction to knot theory inga johnson and allison henrich.
A quantum introduction to knot theory hitoshi murakami abstract. The elementary ideals 72 72 78 86 87 90 94 94 96 100 101 chapter viii the knot polynomials introduction. Adams has also written a comic book about knot theory called why knot. Henrich, ebook format, from the dymocks online bookstore. The bridge number bl of a link lis the smallest integer nsuch that lmay be expressed as the tangle sum of two trivial nstring tangles.
Introduction in the past 50 years, knot theory has become an extremely welldeveloped subject. Read an interactive introduction to knot theory by inga johnson available from rakuten kobo. A tame knot is any knot equivalent to a polygonal knot. The opening chapter offers activities that explore the world of knots and linksincluding games with knots and invites the reader to generate their own questions in knot theory. Knot theory week 1 ucsb 2015 1 introduction outside of mathematics, knots are ways to loop a single piece of string around itself. In knot theory and 3manifold theory, often the adjective tame is omitted.
Ropelength and tight knots jason cantarella university of georgia ictp knot theory summer school, trieste, 2009. Classification and detection of knots concepts from the mathematical field of knot theory have. An interactive introduction to knot theory ebook by inga johnson. Lecture notes class projects course information this is an introductory course in knot theory. This is an introduction to knot theory for nonspecialists, focused on quantum invariants. Henrich this wellwritten and engaging volume, intended for undergraduates, introduces knot theory, an area of growing interest in contemporary mathematics. An interactive introduction to knot theory mathematical. Cornell robotic construction laboratorys log knot 1. Knot theory consists of the study of equivalence classes of knots. Introduction this survey considers three current areas of study that combine the elds of graph theory and knot theory.
Jan 04, 2011 this paper is an introduction to virtual knot theory and an exposition of new ideas and constructions, including the parity bracket polynomial, the arrow polynomial, the parity arrow polynomial. Chapter vii the free calculus and the elementary ideals introduction. Although the subject matter of knot theory is familiar to everyone and its problems are easily stated, arising not only in many branches of mathematics but also in such diverse. I describe the homologies of covering spaces of a knot, the alexander polynomial, the homfly polynomial, the colored jones polynomial, and the volume conjecture. Its very humorous but is a genuine introduction to the mathematics involved. In mathematics, we mean something slightly di erent by a knot.
The basic question one asks in knot theory is, given two knots how to know if they are the same knot or not. Although beyond the scope of this leisurely introduction. An introduction to knot theory and the knot group 5 complement itself could be considered a knot invariant, albeit a very useless one on its own. Cohen set theory and the continuum hypothesis, alfred tarski undecidable theories, gary chartrand introductory graph theory, hermann weyl the concept of a riemann surface, shlomo sternberg dynamical systems. An interactive introduction to knot theory by inga johnson. Buy an interactive introduction to knot theory aurora. For example, consider the following knot projections.
An interactive introduction to knot theory inga johnson, allison k. A spatial embedding of a graph is, informally, a way to place the graph in space. Ropelength minimizers called tight knots exist in each knot and link type and are c1,1. Of all the technical areas in which we publish, dover is most recognized for our magnificent mathematics list. Dover modern math originals rediscovering northwest denver. We have also avoided 4dimensional questions, such as the sliceribbon conjecture problem 1. The majority of the pictures were drawn using inkscape or tikz, with a few exceptions taken from adams, 2004. Knotsintroduction wikibooks, open books for an open world. Gives good explanations of many of the relevant concepts, but does not cover all the material of this course. The central problem of knot theory is determining whether two knots can be rearranged without cutting to be exactly alike.
An interactive introduction to knot theory by inga johnson and allison k henrich topics. We are the home of such worldclass theorists as paul j. This book was written as an introductory text for a onesemester course and, as such, it is far from a comprehensive reference work. An interactive introduction to knot theory an interactive introduction to knot theory inga johnson and allison k. Geometry of alternating links 32 exercises 40 chapters.
Start moving along the knot, as we encounter the crossings we start numbering them, so every crossing has two numbers assigned to it once we have traced the entire knot. Inga johnsons wonderful an interactive introduction to knot theory johnson, 2017. Tejas kalelkar 1 introduction knot theory is the study of mathematical knots. Historically, mathematicians have studied various graph. An introduction to knot theory with 114 illustrations springer.
Knots which are not tame are called wild, and can have pathological behavior. This wellwritten and engaging volume, intended for undergraduates, introduces knot theory, an area of growing interest in contemporary mathematics. An introduction to elementary set theory guram bezhanishvili and eachan landreth 1 introduction in this project we will learn elementary set theory from the original historical sources by two key gures in the development of set theory, georg cantor 18451918 and richard dedekind 18311916. Mathematics in life including gambling and games is described and. This account is an introduction to mathematical knot theory, the theory of knots and links of simple closed curves in threedimensional space. Buy ebook an interactive introduction to knot theory by inga johnson, allison k. An elementary introduction to the mathematical theory of knots. Introduction knot theory is the study of the various properties and behaviors of mathematical knots. Novel aspects of knotplot include interactive construction and manipulation of a large variety of knots and their embeddings into threespace, automated and semiautomated knot relaxation and simplification algorithms, and techniques for calculating and converting among a number of mathematical. Trefoil knot fi g ure 4 c lo sing b ra ids to fo rm k no ts a nd link s. The handson approach features many exercises to be completed by readers. Intuitively if we were to take a piece of string, cord, or the like, tie a knot in it and then glue the loose ends together, we would have a knot. This paper is an introduction to virtual knot theory and an exposition of new ideas and constructions, including the parity bracket polynomial, the arrow polynomial, the parity arrow polynomial. Theory and its applications knot theory mathematical association of america textbooks an interactive introduction to knot theory aurora.
The merit of knot theory for the study of dimensional manifolds consists, first of all, in that every closed oriented dimensional manifold can be represented as a covering of the sphere, ramified over a certain link alexanders theorem. Henrich is the coauthor of a book on knot theory, an interactive introduction to knot theory with inga johnson, dover publications, 2017. This account is an introduction to mathematical knot theory, the theory of knots. A polygonal knot is a knot whose image in r 3 is the union of a finite set of line segments. Read an interactive introduction to knot theory by inga johnson,allison k. The knot group of a knot awith base point b2s3 ima is the fundamental group of the knot complement of a, with bas the base point. A braid is an em b ed d in g of a co llect ion of stran d s th at h ave th eir en d s. Henrich, 9780486804637, available at book depository with free delivery worldwide. Dover modern math originals kindle edition by johnson, inga, henrich, allison k download it once and read it on your kindle device, pc, phones or tablets. Feb 24, 2017 interactive introduction to knot theory by allison k. Polyhedral decomposition of the figure8 knot complement 9. Its history, its people, its landmarks hoods texas brigade, its marches, its.
This comic book comes with a plastic rope that can be knotted, unknotted, and twisted into different shapes. The knot book freeman and company, 2001 an easy to read elementary introduction to knot theory. An introduction to knot theory matt skerritt c9903032 june 27, 2003 1 introduction a knot, mathematically speaking, is a closed curve sitting in three dimensional space that does not intersect itself. Knot theory this chapter looks at some of the fundamental building blocks of knot theory. The focus of this article is this elementary aspect to knot theory.198 395 1214 784 1516 313 501 1229 867 839 568 419 241 313 1071 1175 730 1374 488 274 89 1303 1021 683 1362 1385 1342 1210 294 1207 122 248 273 150 321