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Wednesday, May 20, 2020 | History

2 edition of Studying links via closed braids found in the catalog.

Studying links via closed braids

Joan S. Birman

Studying links via closed braids

by Joan S. Birman

  • 356 Want to read
  • 29 Currently reading

Published by Korea Advanced Institute of Science and Technology, Mathematics Research Center in Taejon, Korea .
Written in English

    Subjects:
  • Braid theory -- Congresses.,
  • Number theory -- Congresses.,
  • Functions, Algebraic -- Congresses.

  • Edition Notes

    Includes bibliographical references.

    Other titlesNumber theory in function fields.
    Statement[Joan Birman]; Number theory in function fields / [Michael Rosen].
    SeriesLecture notes of the ninth KAIST Mathematics Workshop, Lecture notes of the ... KAIST Mathematics Workshop -- 9th.
    ContributionsRosen, Michael I. 1938-, KAIST Mathematics Workshop (9th : 1994).
    Classifications
    LC ClassificationsQA612.23 .B575 1994
    The Physical Object
    Paginationvii, 123 p. :
    Number of Pages123
    ID Numbers
    Open LibraryOL15565479M

    Let ξ be the standard contact structure in oriented \\sl I\\kernptR \\kernpt3=(ρ,θ,z) given as the kernel of the 1-form α=ρ2dθ+dz. A transverse knot is a knot that is transverse to the planes of this contact structure. In this paper we prove the Markov Theorem for transverse knots, which states that two transverse closed braids that are isotopic as transverse knots are also. The Book of Braids: A New Approach to Creating Kumihimo. Author: Jacqui Carey. Over specific examples are used throughout the book to illustrate each point, with the purpose of revealing the concepts behind the making of kumihimo, and explaining how these ideas can be employed to create new designs.

    Colin C. Adams, The knot book, W. H. Freeman and Company, New York, An elementary introduction to the mathematical theory of knots. Studying links via closed braids. IV. Composite links and split links, Invent. Math. American Mathematical Society Charles Street Providence, Rhode Island or Studying links via closed braids III: Classifying links which are closed 3-braids by Joan S. Birman, William, W. Menasco - Pacific J. Math, A complete solution is given to the classification problem for oriented links which are closed three-braids.

    the following description. Transverse knots and links can be represented by closed braids. If we consider the contact manifold (S3;˘ std) described in Chapter 2, then any closed braid around z-axis can be made transverse to the contact planes. Bennequin proved that any transverse link in (S3;˘ std) is transversely isotopic to a closed braid [5].Cited by: 1. This book provides a comprehensive exposition of the theory of braids, beginning with the basic mathematical definitions and structures. Among the many topics explained in detail are: the braid group for various surfaces; the solution of the word problem for the braid group; braids in the context of knots and links (Alexander's theorem); Markov's theorem and its use in obtaining .


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Studying links via closed braids by Joan S. Birman Download PDF EPUB FB2

Pacific J. Math. VolumeNumber 1 (), Studying links via closed braids. III. Classifying links which are closed $3$-braids. Joan S. Birman and William W. MenascoCited by: STUDYING LINKS VIA CLOSED BRAIDS I: A FINITENESS THEOREM.

by Joan S. Birman and William W. Menasco §1 Introduction. This paper is the first in a series of papers in. STUDYING LINKS VIA CLOSED BRAIDS I: A FINITENESS THEOREM JOAN S. BIRMAN AND WILLIAM W. MENASCO This paper is the first in a series which study the closed braid rep-resentatives of an oriented link type 2.

in oriented 3-space. A combi-natorial symbol is introduced which determines an oriented spanning surface F for a representative L of 3?. The. This is an Erratum to "Studying Links Vai Closed Braids IV: Composite Links and Split Links", Inventiones Math., Facs. 1 (), Discover the world's research 17+ million members.

Birman, J.S., Menasco, W.W.: Studying Links Via Closed Braids V: Closed Braid Representatives of the Unlink. Trans. Math. Soc.– () Google ScholarCited by: If the address matches an existing account you will receive an email with instructions to reset your passwordCited by: Get this from a library.

Properties of closed 3-braids and braid representations of links. [Alexander Stoimenow] -- This book studies diverse aspects of braid representations via knots and links. Complete classification results are illustrated for several properties through Xu's normal 3-braid form and the Hecke.

The purpose of the Association for Women in Mathematics is to encourage women and girls to study and to have active careers in the mathematical sciences, and to promote equal opportunity and the equal treatment of women and girls in the mathematical sciences.

Joan S. Birman. Studying Links via Braids. One approach to this problem is to study links via the nested sequence of braid groups.

Since each link can be represented as a closed braid, and since braids form a group, this approach allows one to utilize familiar group invariants, such as group characters.

We introduce essential open book foliations by refining open book foliations, and develop technical estimates of the fractional Dehn twist coefficient (FDTC) of monodromies and the FDTC for closed braids, which we introduce as well. As applications, we quantitatively study the ‘gap’ between overtwisted contact structures and non-right-veering by: 9.

On a relation between the self-linking number and the braid index of closed braids in open books. Tetsuya Ito Keywords self-linking number closed braid open book foliation Jones–Kawamuro conjecture. Studying links via closed braids, IV: Composite links and split links, Invent.

: Tetsuya Ito. Lecturer: Joan S. Birman Studying Links via Braids Joan S. Birman received her BA in mathematics in from Barnard College of Columbia University and her MA in physics two years later from Columbia. After several years of working as a systems analyst in the aircraft industry, she took a temporary break and devoted her energies to raising three children.

Joan Birman and William Menasco, Studying links via closed braids V: the unlink, Trans. AMS, (2)-- Joan Birman, Marta Rampichini, Paolo Boldi, and Sebastiano Vigna, Towards an Implementation of the B-H algorithm for recognizing the unknot, J. Knot Theory and Its Ramifications, 11 (4) A Study of Braids (Mathematics and Its Applications) th Edition This was one of the motivations Artin had in mind when he began studying braid theory.

In Chap we discuss the primary applications of braid theory to knot theory, including the introduction of the most important invariants of knot theory, the Alexander polynomial and Cited by: Studying links via closed braids IV: composite links and split links Proof.

To simplify notation we consider a special case, assuming that: • The negative singularity of R,theb-arcs in R, and the positive singularity of R occur in that order in the fibration.

• The puncture point R ∪K is positive. We will establish that the order of the positive puncture and the positive. @article{4, mrkey = {}, author = {Birman, Joan S. and Menasco, William W.}, title = {Studying links via closed braids. {IV}. {C}omposite links and split links},Cited by: Two papers are in preparation.

References [I] J.S. Birman, Braids, Links and Mapping Class Groups, Annals of Mathematics Studies 82 (Princeton University Press, Princeton, NJ, ). [2] J.S. Birman and W.W. Menasco, Studying links via closed braids IV: Composite links and split links. Invent.

Math. () [3]Cited by: Joan Sylvia Lyttle Birman (born in New York City) is an American mathematician, specializing in low-dimensional has made contributions to the study of knots, 3-manifolds, mapping class groups of surfaces, geometric group theory, contact structures and dynamical is currently Research Professor Emerita at Barnard College, Alma mater: B.A., Barnard College,Ph.D.

We give an alternative proof of a theorem of Honda-Kazez-Matić that every non-right-veering open book supports an overtwisted contact structure. We also study two types of examples that show how overtwisted discs are embedded relative to right-veering open books.

Hair: A Book of Braiding and Styles Spiral-bound – March 1, You could call it "Braids & More for Dummies." The book is NOT childish or smart-alecky. The scrunchies that are attached to the front of the book are not pretty, but it's a thoughtful Klutz trademark that they usually attach some item related to the book's contents.

/5(). Further classifications of knots and links arising by the closure of 3-braids are given, and new results about 4-braids are part of the work.

Written with knot theorists, topologists,and graduate students in mind, this book features the identification and analysis of effective techniques for diagrammatic examples with unexpected properties.J.

Birman and W. Menasco "Studying links via closed braids. III: Classifying links which are closed 3-braids" Pacific J. Math. Crossref Google Scholar.Knots, braids, and mapping class groups--papers dedicated to Joan S.

Birman: proceedings of a conference on low dimensional topology in honor of Joan S. Birman's 70th birthday, March, Columbia University, New York, New York Joan S. Birman, Jane Gilman, William W. Menasco, Xiao-Song Lin.