2008/05/16 by Noah Kieserman, Kieserman, Noah
Computer Science · Engineering · Mathematics · #32G10 #57R30 #70G45 #Advanced Mathematical Modeling in Engineering #Elasticity and Material Modeling #Elasticity and Wave Propagation #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG) #math.GT #math.SG #msc:32G10 #msc:57R30 #msc:70G45
paper · pdf · doi:10.48550/arxiv.0805.2468
27 pages, 3 figures
arxiv created 2008/05/16 · openalex publication_date 2008/05/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The work of Oh and Park ([OP]) on the deformation problem of coisotropic submanifolds opened the possibility of studying a large and interesting class of foliations with some explicit geometric tools. These tools assemble into the structure of an L-infinity algebra on the shifted foliation complex (Ω^*[1](\fol), d_\fol), which allows a concise description of deformations in terms of a Maurer-Cartan equation. Infinitesimal deformations are given by d_\fol-closed forms, and the relation between infinitesimal deformations and full deformations can be studied in terms of obstruction classes lying in the foliation cohomology H^*_\fol. Closely related to the foliation cohomology is Haefliger's group Ω^*c(T/H), an under-appreciated model for the leaf space of a foliation. We make integral use of this group in showing solvability and unsolvability of the obstruction equations. We also show the L-infinity apparatus to be capable of detecting the Liouville/diophantine distinction of KAM theory, and argue for the greater significance of Haefliger's integration-over-leaves map in passing this fine structure to a geometric model for the leaf space.