Families of Legendrian Submanifolds via Generating Families

2013/11/03 by Sabloff, Joshua M., Sullivan, Michael G.
#57Q45 #57R17 #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1311.0528

Abstract

We investigate families of Legendrian submanifolds of 1-jet spaces by developing and applying a theory of families of generating family homologies. This theory allows us to detect an infinite family of loops of Legendrian n-spheres embedded in the standard contact (2n+1)-space (for n>1) that are contractible in the smooth, but not Legendrian, categories.

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