Techniques for Proving Intrinsic Flat Limits are not the Zero Space

Emerging Topics on Scalar Curvature and Convergence
Topic:Techniques for Proving Intrinsic Flat Limits are not the Zero Space
Speaker:Christina Sormani
Affiliation:City University of New York; Visitor, School of Mathematics
Date:Wednesday, February 27
Time/Room:10:00am - 11:00am/Simonyi Hall 112

Last Fall the Emerging Topics on Scalar Curvature and Convergence group discussed and devised a number of conjectures concerning the intrinsic flat limits of sequences of manifolds with lower bounds on their scalar curvature. Many of these were almost rigidity conjectures that a sequence of M_j almost satisfying a variety of hypotheses must converge in the intrinsic flat sense to a limit space M_\infty which is rigidly determined by actually satisfying those hypotheses. A first step towards proving such a theorem if the sequence has volume and diameter from above is to apply Wenger's Compactness Theorem to produce a limit space. However this limit could be the 0 space. In this talk, I will present a variety of theorems proven in S-Wenger, Portegies-S, Matveev-Portegies, Perales, Huang-Lee-S, Allen-S, Perales-Nunez, Cabrera-Ketterer-Perales, and Allen-Bryden which can be applied to prove the limit space is nonzero. For the most part these theorems are hidden within papers proving almost rigidity theorems.