The persistence of the Chekanov–Eliashberg algebra

Selecta Mathematica - Tập 26 - Trang 1-32 - 2020
Georgios Dimitroglou Rizell1, Michael G. Sullivan2
1Department of Mathematics, Uppsala University, Uppsala, Sweden
2Department of Mathematics and Statistics, University of Massachusetts, Amherst, USA

Tóm tắt

We apply the barcodes of persistent homology theory to the c Chekanov–Eliashberg algebra of a Legendrian submanifold to deduce displacement energy bounds for arbitrary Legendrians. We do not require the full Chekanov–Eliashberg algebra to admit an augmentation as we linearize the algebra only below a certain action level. As an application we show that it is not possible to $$C^0$$ -approximate a stabilized Legendrian by a Legendrian that admits an augmentation.

Tài liệu tham khảo

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