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!

• The Blue Phases: Introduction
• What Are Liquid Crystals?
• Order Parameter Fields
• Defects in Nematic Liquids
• Homotopy Theory and Defects
• Parallel Transport and Energy
• Twisted Parallelism: Chiral Nematics
• Chiral Nematic Phases: Helical and Blue
• Blue Phases: Networks of Defect Lines
• Defect Lines and Frustration: Curved Space

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Sethna's Research 90-94

Entertaining Science done at

LASSP.

James P. Sethna, sethna@lassp.cornell.edu

Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).