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Borromean and Brunnian rings - Page d'accueil / Lirmm.fr ... · Borromean and Brunnian rings ......

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Borromean and Brunnian rings Rade Živaljević Mathematical Institute SANU, Belgrade Centre for Dynamical Systems, Geometry and Combinatorics
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Page 1: Borromean and Brunnian rings - Page d'accueil / Lirmm.fr ... · Borromean and Brunnian rings ... Handbook of discrete and . computational geometry. J. E. Goodman,J. O'Rourke. Editors.

Borromean and Brunnian rings

Rade ŽivaljevićMathematical Institute SANU, Belgrade

Centre for Dynamical Systems, Geometry and Combinatorics

Page 2: Borromean and Brunnian rings - Page d'accueil / Lirmm.fr ... · Borromean and Brunnian rings ... Handbook of discrete and . computational geometry. J. E. Goodman,J. O'Rourke. Editors.

Dušan ŽivaljevićAnimated by

http://vimeo.com/9802595

Page 3: Borromean and Brunnian rings - Page d'accueil / Lirmm.fr ... · Borromean and Brunnian rings ... Handbook of discrete and . computational geometry. J. E. Goodman,J. O'Rourke. Editors.

VideoDusan.Zivaljevic-Final.2

Page 4: Borromean and Brunnian rings - Page d'accueil / Lirmm.fr ... · Borromean and Brunnian rings ... Handbook of discrete and . computational geometry. J. E. Goodman,J. O'Rourke. Editors.

Borromean ringsLogo of the

International Mathematical UnionIMU

Page 5: Borromean and Brunnian rings - Page d'accueil / Lirmm.fr ... · Borromean and Brunnian rings ... Handbook of discrete and . computational geometry. J. E. Goodman,J. O'Rourke. Editors.

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Page 6: Borromean and Brunnian rings - Page d'accueil / Lirmm.fr ... · Borromean and Brunnian rings ... Handbook of discrete and . computational geometry. J. E. Goodman,J. O'Rourke. Editors.

How to Hang a Painting

There's more to hanging a painting than just driving a nail in the wall. Picture wire should distribute the weight so the canvas won't sag. ............

http://www.ehow.com/how_2124056_hang-painting.html

Page 7: Borromean and Brunnian rings - Page d'accueil / Lirmm.fr ... · Borromean and Brunnian rings ... Handbook of discrete and . computational geometry. J. E. Goodman,J. O'Rourke. Editors.
Page 8: Borromean and Brunnian rings - Page d'accueil / Lirmm.fr ... · Borromean and Brunnian rings ... Handbook of discrete and . computational geometry. J. E. Goodman,J. O'Rourke. Editors.

ab ab a b = [a,b ]-1 -1 -1

Page 9: Borromean and Brunnian rings - Page d'accueil / Lirmm.fr ... · Borromean and Brunnian rings ... Handbook of discrete and . computational geometry. J. E. Goodman,J. O'Rourke. Editors.
Page 10: Borromean and Brunnian rings - Page d'accueil / Lirmm.fr ... · Borromean and Brunnian rings ... Handbook of discrete and . computational geometry. J. E. Goodman,J. O'Rourke. Editors.

a b a b d c d c b a b a c d c d1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2

-1 -1 -1 -1-1 -1 -1 -1

Page 11: Borromean and Brunnian rings - Page d'accueil / Lirmm.fr ... · Borromean and Brunnian rings ... Handbook of discrete and . computational geometry. J. E. Goodman,J. O'Rourke. Editors.

VideoDusan.Zivaljevic-Final.2

Page 12: Borromean and Brunnian rings - Page d'accueil / Lirmm.fr ... · Borromean and Brunnian rings ... Handbook of discrete and . computational geometry. J. E. Goodman,J. O'Rourke. Editors.

Handbook of discrete and computational geometryJ.

E. Goodman,J. O'Rourke

EditorsCRC Press 2004

Page 13: Borromean and Brunnian rings - Page d'accueil / Lirmm.fr ... · Borromean and Brunnian rings ... Handbook of discrete and . computational geometry. J. E. Goodman,J. O'Rourke. Editors.

R. Živaljević. Topological Methods.

Chapter 14, Handbook of Discrete and Computational Geometry

Configuration space-test map scheme for applications of topological methods in geometric combinatorics.

Page 14: Borromean and Brunnian rings - Page d'accueil / Lirmm.fr ... · Borromean and Brunnian rings ... Handbook of discrete and . computational geometry. J. E. Goodman,J. O'Rourke. Editors.

CONFIGURATION SPACE-TEST MAP SCHEME

CSTM-scheme is a general topological method for solving problems in combinatorics

and discrete geometry relevant for compu-tational

geometry, analysis of algorithms and computational mathematics in general.

Page 15: Borromean and Brunnian rings - Page d'accueil / Lirmm.fr ... · Borromean and Brunnian rings ... Handbook of discrete and . computational geometry. J. E. Goodman,J. O'Rourke. Editors.

CONFIGURATION SPACE-TEST MAP SCHEME

Key words and phrases:

(a) configuration spaces (b) test spaces(c) (equivariant) test maps

Equivariant

topological methods in geometric combinatorics


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