---
res:
bibo_abstract:
- "Two smooth map germs are right-equivalent if and only if they generate two\r\nLagrangian
submanifolds in a cotangent bundle which have the same contact with\r\nthe zero-section.
In this paper we provide a reverse direction to this\r\nclassical result of Golubitsky
and Guillemin. Two Lagrangian submanifolds of a\r\nsymplectic manifold have the
same contact with a third Lagrangian submanifold\r\nif and only if the intersection
problems correspond to stably right equivalent\r\nmap germs. We, therefore, obtain
a correspondence between local Lagrangian\r\nintersection problems and catastrophe
theory while the classical version only\r\ncaptures tangential intersections.
The correspondence is defined independently\r\nof any Lagrangian fibration of
the ambient symplectic manifold, in contrast to\r\nother classical results. Moreover,
we provide an extension of the\r\ncorrespondence to families of local Lagrangian
intersection problems. This\r\ngives rise to a framework which allows a natural
transportation of the notions\r\nof catastrophe theory such as stability, unfolding
and (uni-)versality to the\r\ngeometric setting such that we obtain a classification
of families of local\r\nLagrangian intersection problems. An application is the
classification of\r\nLagrangian boundary value problems for symplectic maps.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Christian
foaf_name: Offen, Christian
foaf_surname: Offen
foaf_workInfoHomepage: http://www.librecat.org/personId=85279
orcid: https://orcid.org/0000-0002-5940-8057
dct_date: 2018^xs_gYear
dct_language: eng
dct_title: Local intersections of Lagrangian manifolds correspond to catastrophe theory@
...