Defects and Homotopy Theory
(61)

 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
homotopy class

is integers mod 2: +1/2 are equivalent! 
More about
Order Parameters, Broken Symmetry, and Topology.
This research was paid for by THE US GOVERNMENT
by the NSF.
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Sethna's Research 9094

Entertaining Science done at

LASSP.
Last modified: November 2, 1995
James P. Sethna,
sethna@lassp.cornell.edu
Statistical Mechanics: Entropy, Order Parameters, and Complexity,
now available at
Oxford University Press
(USA,
Europe).