nLab Ambidexterity in K(n)-Local Stable Homotopy Theory

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Stable Homotopy theory

This page collects some links related to

Michael Hopkins, Jacob Lurie:

Ambidexterity in $K(n)$ -Local Stable Homotopy Theory

(2013)

pdf

also: talk at Notre Dame Graduate Summer School on Topology and Field Theories and Harvard lecture 2012 (video part 1, part 2, part 3 part 4, pdf lecture notes by Chris Elliott)

on bilimits in K(n)-local stable homotopy theory and generally on ambidextrous adjunctions and their un-twisted Wirthmüller isomorphisms for ∞-module bundles in semiadditive (∞,1)-categories.

(The untwisted Wirthmüller isomorphism is the map $\mu$ in Construction 4.0.7 and then the norm map in Remark 4.1.12. The induced integration map considered in Construction 4.0.7, Notation 4.1.6 there is also discussed (for the general twisted case) in the article Quantization via Linear homotopy types, see section 4.3 there for details.)

The discussion in the article is apparently motivated as part of what it takes to make precise the discussion of quantization in sections 3 and 8 of

Dan Freed, Mike Hopkins, Jacob Lurie, Constantin Teleman, Topological Quantum Field Theories from Compact Lie Groups in P. R. Kotiuga (ed.) A celebration of the mathematical legacy of Raoul Bott AMS (2010) (arXiv:0905.0731)

For the 2014 installment of UOregon’s Moursund Lecture Series, Jacob Lurie gave three (video recorded) lectures on spectral algebraic geometry, one of which is