The cardinality of the augmentation category of a Legendrian link

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Title: The cardinality of the augmentation category of a Legendrian link
Authors: Ng, L
Rutherford, D
Shende, V
Sivek, S
Item Type: Working Paper
Abstract: We introduce a notion of cardinality for the augmentation category associated to a Legendrian knot or link in standard contact R^3. This `homotopy cardinality' is an invariant of the category and allows for a weighted count of augmentations, which we prove to be determined by the ruling polynomial of the link. We present an application to the augmentation category of doubly Lagrangian slice knots.
Issue Date: 31-Dec-2017
URI: http://hdl.handle.net/10044/1/52047
Copyright Statement: © 2015 The Authors
Keywords: math.SG
math.GT
Notes: 15 pages
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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