76 research outputs found
The Minimal Length of a Lagrangian Cobordism between Legendrians
To investigate the rigidity and flexibility of Lagrangian cobordisms between
Legendrian submanifolds, we investigate the minimal length of such a cobordism,
which is a -dimensional measurement of the non-cylindrical portion of the
cobordism. Our primary tool is a set of real-valued capacities for a Legendrian
submanifold, which are derived from a filtered version of Legendrian Contact
Homology. Relationships between capacities of Legendrians at the ends of a
Lagrangian cobordism yield lower bounds on the length of the cobordism. We
apply the capacities to Lagrangian cobordisms realizing vertical dilations
(which may be arbitrarily short) and contractions (whose lengths are bounded
below). We also study the interaction between length and the linking of
multiple cobordisms as well as the lengths of cobordisms derived from
non-trivial loops of Legendrian isotopies.Comment: 33 pages, 9 figures. v2: Minor corrections in response to referee
comments. More general statement in Proposition 3.3 and some reorganization
at the end of Section
Recommended from our members
An Introduction to Seshat: Global History Databank
This article introduces the Seshat: Global History Databank, its potential, and its methodology. Seshat is a databank containing vast amounts of quantitative data buttressed by qualitative nuance for a large sample of historical and archaeological polities. Thee sample is global in scope and covers the period from the Neolithic Revolution to the Industrial Revolution. Seshat allows scholars to capture dynamic processes and to test theories about the co-evolution (or not) of social scale and complexity, agriculture, warfare, religion, and any number of such Big Questions. Seshat is rapidly becoming a massive resource for innovative cross-cultural and cross-disciplinary research. Seshat is part of a growing trend to use comparative historical data on a large scale and contributes as such to a growing consilience between the humanities and social sciences. Seshat is underpinned by a robust and transparent workflow to ensure the ever growing dataset is of high quality
- …