Mathematics Colloquium

Thursday, December 1, 2016
4:20 PM - 5:20 PM (ET)
Exley Science Center Tower ESC 121
Event Type
Canalia, Caryn

Karen Melnick, University of Maryland: Limits of local autommorphisms of geometric structures


Abstract: The automorphism group of a rigid geometric structure is a Lie group.  In fact, the local automorphisms form a Lie pseudogroup; this property is often taken as an informal definition of rigid geometric structure.  In which topology is this the case?  The classical theorems of Myers and Steenrod say that $C^0$ convergence of local isometries of a smooth Riemannian metric implies $C^\infty$ convergence; in particular, the compact-open and $C^\infty$ topologies coincide on the isometry group.  I will present joint results with C. Frances in which we prove the same result for local automorphisms of smooth parabolic geometries, a rich class of geometric structures including conformal and projective structures.  

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