#### Document Type

Article

#### Abstract

The extended power construction can be used to create new framed manifolds out of old. We show here how to compute the effect of such operations in the Adams spectral sequence, extending partial results of Milgram and the author. This gives the simplest method of proving that Jones’ 30-manifold has Kervaire invariant one, and allows the construction of manifolds representing Mahowald’s classes η4 and η5, among others.

#### Disciplines

Algebraic Geometry | Geometry and Topology

#### Recommended Citation

Bruner, R. R. Extended powers of manifolds and the Adams spectral sequence. In J.P.C. Greenlee, R.R. Bruner, & N. Kuhn, Eds. Homotopy methods in algebraic topology. Contemp. Math. 271, 41-51 (2001). Providence, RI: American Mathematical Society.

## Comments

Author's Accepted Manuscript. © Copyright 2001 American Mathematical Society, first published in J.P.C. Greenlee, R.R. Bruner, & N. Kuhn, Eds. Homotopy methods in algebraic topology. Contemp. Math. 271, 41-51 (2001). Providence, RI: American Mathematical Society.