A comparison of norm maps

Abstract

We present a spectrum-level version of the norm map in equivariant homotopy theory based on the algebraic construction in work of Greenleess-May. We show that this new norm map is same as the construction in work Hill-Hopkins-Ravenel on the Kervaire invariant problem. Our comparison of the two norm maps gives a conceptual understanding of the choices inherent in the definition of the multiplicative norm map.

11 pages; with appendix by Anna Marie Bohmann and Emily Riehl

References in corpus (2)

• Higher Topos Theory
• On the non-existence of elements of Kervaire invariant one

Cited by in corpus (2)

• Cyclotomic structure in the topological Hochschild homology of $DX$
• Bi-incomplete Tambara functors as $\mathcal{O}$-commutative monoids