Project description
This project concerns the study of bordism classes of smooth manifolds with specified tangential structures (e.g. oriented, Spin, and String manifolds). These are manifolds equipped with a reduction of the structure groups of their respective stable tangent bundles to a k-connected cover of the infinite orthogonal group. As k varies, these bordism theories interpolate between unoriented and framed bordism. We are particularly interested in the case where k is large and the dimension of the manifolds under consideration is bounded by an exponentially increasing function of k. A key part of this analysis is the interplay between commutative algebra structures on the representing spectra and nilpotence phenomena.Related publications
Published articles
Akhil Mathew, Niko Naumann and Justin Noel, Nilpotence and descent in equivariant stable homotopy theory. Advances in Mathematics, vol.\ 305, pp.\ 994-1084, January 2017.
Tobias Barthel, Markus Hausmann, Niko Naumann and Justin Noel, Thomas Nikolaus, and Nathaniel Stapleton The Balmer spectrum of the equivariant homotopy category of a finite abelian group. Invent. Math. 216 (2019), no. 1, 215–240.
Akhil Mathew, Niko Naumann and Justin Noel, Derived induction and restriction theory. Geom. Topol. 23 (2019), no. 2, 541–636
Dustin Clausen, Akhil Mathew, Niko Naumann and Justin Noel, Descent in algebraic $K$-theory and a conjecture of Ausoni-Rognes. J. Eur. Math. Soc. (JEMS) 22 (2020), no. 4, 1149–1200.