Defects and Homotopy Theory
- Encircle line defect with curve C
- n maps C into curve onto projective plane
- Homotopy Group
- First Homotopy Group is Equivalence Classes of Topologically Distinct
Curves (can't be deformed into one another)
- Two defects inequivalent if surrounding curves differ in
||is integers mod 2: +-1/2 are equivalent!
Order Parameters, Broken Symmetry, and Topology.
This research was paid for by THE US GOVERNMENT
by the NSF.
Sethna's Research 90-94
Entertaining Science done at
Last modified: November 2, 1995
James P. Sethna,
Statistical Mechanics: Entropy, Order Parameters, and Complexity,
now available at
Oxford University Press