2020/10/19 by Burklund, Robert, Hahn, Jeremy, Senger, Andrew
#Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2010.09869
We prove that the inertia groups of all sufficiently-connected, high-dimensional (2n)-manifolds are trivial. This is a key step toward a general classification of manifolds in the metastable range. Specifically, for m ≫ 0 and k>5/12, suppose M is a \lfloor km \rfloor-connected, smooth, closed, oriented m-manifold and Σ is an exotic m-sphere. We prove that, if M \sharp Σ is diffeomorphic to M, then Σ bounds a parallelizable manifold. Our proof is built on an understanding of the second extended power functor in Pstrągowski's category of synthetic spectra.