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1/3 Introduction to knot contact homology

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1/3 Introduction to knot contact homology
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36
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CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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We define knot contact homology as the Legendrian differential graded algebra of the unit conormal lift of a knot. We show how to compute it for knots in the three sphere using flow trees and discuss some of its basic properties. We also introduce the augmentation variety.