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Tautological rings for high-dimensional manifolds
(Cambridge University PressCompositio Mathematica, 2017-04)
We study tautological rings for high-dimensional manifolds, that is, for each smooth manifold $M$ the ring $R^*$($M$) of those characteristic classes of smooth fibre bundles with fibre $M$ which is generated by generalised ...
An upper bound for the pseudoisotopy stable range
(SpringerMathematische Annalen, 2017-08-01)
We prove that the pseudoisotopy stable range for manifolds of dimension 2n can be no better than (2n - 2). In order to do so, we define new characteristic classes for block bundles, extending our earlier work with Ebert, ...
Homological stability for spaces of embedded surfaces
(Mathematical Sciences PublisherGeometry and Topology, 2017-05-10)
© 2017, Mathematical Sciences Publishers. All rights reserved.We study the space of oriented genus-g subsurfaces of a fixed manifold M and, in particular, its homological properties. We construct a “scanning map” which ...
Infinite loop spaces and positive scalar curvature
(SpringerInventiones Mathematicae, 2017-09-01)
We study the homotopy type of the space of metrics of positive scalar curvature on high-dimensional compact spin manifolds. Hitchin used the fact that there are no harmonic spinors on a manifold with positive scalar curvature ...
Homological stability for automorphism groups
(Academic PressAdvances in Mathematics, 2017-10-01)
Given a family of groups admitting a braided monoidal structure (satisfying mild assumptions) we construct a family of spaces on which the groups act and whose connectivity yields, via a classical argument of Quillen, ...