# The Bousfield-Kuhn functor and Topological Andre-Quillen cohomology

@inproceedings{Behrens2017TheBF, title={The Bousfield-Kuhn functor and Topological Andre-Quillen cohomology}, author={Mark Behrens and Charles Rezk}, year={2017} }

We construct a natural transformation from the Bousfield-Kuhn functor evaluated on a space to the Topological Andre-Quillen cohomology of the K(n)-local Spanier-Whitehead dual of the space, and show that the map is an equivalence in the case where the space is a sphere. This results in a method for computing unstable v_n-periodic homotopy groups of spheres from their Morava E-cohomology (as modules over the Dyer-Lashof algebra of Morava E-theory). We relate the resulting algebraic computations… CONTINUE READING

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## Lie algebras and $v_n$-periodic spaces

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CITES BACKGROUND & RESULTS

HIGHLY INFLUENCED

## Spectral algebra models of unstable v_n-periodic homotopy theory

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CITES METHODS & BACKGROUND

## Lie algebra models for unstable homotopy theory.

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## The $v_n$-periodic Goodwillie tower on Wedges and Cofibres

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CITES METHODS

## Completed power operations for Morava E–theory

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## Proposal : Periodic Homotopy Theory of Unstable Spheres

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