MATH 7590 Geometric Topology

Spring 2012

Course Information

Course: MATH 7590 Geometric Topology - Topological Robotics
Time/Place: Tuesday & Thursday, 10:40 am - 12:00 noon, in 276 Lockett
Instructor: Dan Cohen
Office Hours: Tuesday & Thursday, 9:00 - 10:30 am, in 372 Lockett,
and by appointment
Prerequisites: MATH 7512
Grade: Based on an in-class presentation. Some potential presentation topics will be posted.
Text:
 
  		Much of the subject matter may be found in Farber's book "Invitation to Topological Robotics"
This and other potential sources for material covered in this course will be posted.

Course Description

This subject, part of what one might call "applied algebraic topology", is a relatively new area studying topological problems inspired by robotics and engineering, as well as problems of robotics requiring topological tools.

Topics we will pursue in the course include configuration spaces of various types (e.g., configuration spaces of points in the plane or on a surface, configuration spaces of linkages), and the motion planning problem from robotics.

Tools we will use include cohomology theory and Morse theory.

Quadrangles

Mathematica generated movies attempting to illustrate the topology of the configuration space Ml of planar 4-gons for various length vectors l = (l1, l2, l3, l4):
l = (3, 2, 1, 1) l = (3, 2, 2, 1) l = (4, 3, 3, 1) l = (3, 3, 2, 1) l = (2, 2, 1, 1) l = (1, 1, 1, 1)
Department of Mathematics
Louisiana State University
Baton Rouge, LA, 70803
Office: 372 Lockett
Phone: (225) 578-1576
Email: cohen@math.lsu.edu