1 / 97

Lectures on the Geometry and Topology of Configuration Spaces

Lectures on the Geometry and Topology of Configuration Spaces. Sadok Kallel American University of Sharjah (UAE). Introduction. If you type ``configuration spaces" on the archives, you get nearly 300 references. You get many more on Google .

tynice
Download Presentation

Lectures on the Geometry and Topology of Configuration Spaces

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Lectures on the Geometry and Topology of Configuration Spaces SadokKallel American University of Sharjah (UAE)

  2. Introduction If you type ``configuration spaces" on the archives, you get nearly 300 references. You get many more on Google. Configuration Spaces have been used in Topology at least since the early 50’s (particularly as applied to embedding problems). There are configuration spaces in geometry and topology, with applications to physics and various other parts of mathematics. This will be our focus. There are configuration spaces of mechanical systems.

  3. PART 1:CONSTRUCTIONS AND EXAMPLES Theorems change. Examples Remain. Marshall Hall

  4. The configuration space (or C-Space) is the set of all admissible positions of the object. CONFIGURATION SPACES IN MECHANICS

  5. The configuration space of all two legged arms with revolute joints is

  6. Configuration Space Obstacle

  7. Planar Linkages

  8. Configuration Spaces in Topology • . • . • .

  9. The topology of F(X,n) is very rich, even for low values of n

  10. Examples

  11. Show that

  12. Unordered or Unlabeled Configurations

  13. B(C,3) and the trefoil knot

  14. Fadell-NeuwirthFibrations

  15. Proof of the Fadell-Neuwirth Bundle Theorem

  16. Applications

  17. Configurations and Braid Groups

  18. The Dirac Problem

  19. PART 2: APPLICATIONS

  20. Configurations on Graphs

  21. 2 AGV’s on T-graph

  22. Other computations How do weunderstand the homotopy type of F(G,2) in general ?

More Related