Proves a nilpotence theorem for rational rigid 2-rings of moderate growth and shows such categories have enough tt-fields of the form Perf(L) for even 2-periodic fields L.
The Cobordism Hypothesis in Dimension 1
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abstract
In 2009 Lurie published an expository article outlining a proof for a higher version of the cobordism hypothesis conjectured by Baez and Dolan in 1995. In this note we give a proof for the 1-dimensional case of this conjecture. The proof follows most of the outline given in Lurie's paper, but differs in a few crucial details. In particular, the proof makes use of the theory of quasi-unital $\infty$-categories as developed by the author in a previous note.
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A Nilpotence Theorem for Rational Rigid 2-Rings of Moderate Growth
Proves a nilpotence theorem for rational rigid 2-rings of moderate growth and shows such categories have enough tt-fields of the form Perf(L) for even 2-periodic fields L.