A note on geography of bilinearized Legendrian contact homology for disconnected Legendrian submanifolds
Filip Strako\v{s}
TL;DR
This paper establishes a criterion for DGA-homotopy of augmentations in Legendrian contact homology and extends existing geography results to disconnected Legendrian submanifolds, enhancing understanding of their algebraic invariants.
Contribution
It introduces a new criterion for DGA-homotopy of augmentations and applies it to extend geography results to disconnected Legendrian submanifolds.
Findings
Criterion for DGA-homotopy of augmentations
Extension of geography results to disconnected cases
Enhanced understanding of Legendrian contact homology invariants
Abstract
In this short note, we provide a criterion for DGA-homotopy of augmentations of Chekanov-Eliashberg algebra of disconnected Legendrian submanifolds. We apply the criterion to obtain the extension of geography results of Bourgeois and Galant concerning bilinearized Legendrian contact homology to the case of disconnected Legendrian submanifolds.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology