Udvidet returret til d. 31. januar 2025

Braids, Links, and Mapping Class Groups. (AM-82), Volume 82

Bag om Braids, Links, and Mapping Class Groups. (AM-82), Volume 82

The central theme of this study is Artin's braid group and the many ways that the notion of a braid has proved to be important in low-dimensional topology. In Chapter 1 the author is concerned with the concept of a braid as a group of motions of points in a manifold. She studies structural and algebraic properties of the braid groups of two manifolds, and derives systems of defining relations for the braid groups of the plane and sphere. In Chapter 2 she focuses on the connections between the classical braid group and the classical knot problem. After reviewing basic results she proceeds to an exploration of some possible implications of the Garside and Markov theorems. Chapter 3 offers discussion of matrix representations of the free group and of subgroups of the automorphism group of the free group. These ideas come to a focus in the difficult open question of whether Burau's matrix representation of the braid group is faithful. Chapter 4 is a broad view of recent results on the connections between braid groups and mapping class groups of surfaces. Chapter 5 contains a brief discussion of the theory of "plats." Research problems are included in an appendix.

Vis mere
  • Sprog:
  • Engelsk
  • ISBN:
  • 9780691081496
  • Indbinding:
  • Paperback
  • Sideantal:
  • 237
  • Udgivet:
  • 21. februar 1975
  • Størrelse:
  • 152x229x13 mm.
  • Vægt:
  • 312 g.
  • BLACK WEEK
  Gratis fragt
Leveringstid: 8-11 hverdage
Forventet levering: 9. december 2024

Beskrivelse af Braids, Links, and Mapping Class Groups. (AM-82), Volume 82

The central theme of this study is Artin's braid group and the many ways that the notion of a braid has proved to be important in low-dimensional topology.
In Chapter 1 the author is concerned with the concept of a braid as a group of motions of points in a manifold. She studies structural and algebraic properties of the braid groups of two manifolds, and derives systems of defining relations for the braid groups of the plane and sphere. In Chapter 2 she focuses on the connections between the classical braid group and the classical knot problem. After reviewing basic results she proceeds to an exploration of some possible implications of the Garside and Markov theorems.

Chapter 3 offers discussion of matrix representations of the free group and of subgroups of the automorphism group of the free group. These ideas come to a focus in the difficult open question of whether Burau's matrix representation of the braid group is faithful. Chapter 4 is a broad view of recent results on the connections between braid groups and mapping class groups of surfaces. Chapter 5 contains a brief discussion of the theory of "plats." Research problems are included in an appendix.

Brugerbedømmelser af Braids, Links, and Mapping Class Groups. (AM-82), Volume 82



Find lignende bøger
Bogen Braids, Links, and Mapping Class Groups. (AM-82), Volume 82 findes i følgende kategorier:

Gør som tusindvis af andre bogelskere

Tilmeld dig nyhedsbrevet og få gode tilbud og inspiration til din næste læsning.