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4 votes
0 answers
226 views

How to to understand the homology groups $H_*(\Omega_0^\infty S^\infty)$?

The original statement of the Barratt--Priddy theorem says there is an isomorphism of homology groups $$H_*(\Sigma_\infty)\cong H_*(\Omega_0^\infty S^\infty),$$ where $\Omega_0^\infty S^\infty$ is the ...
11 votes
2 answers
864 views

Solving polynomial equations in spectra?

Let $M$ be the mod-$p$ Moore spectrum where $p \geq 3$ is a (power of) a prime. Then $M$ satisfies the "polynomial equation" $M \wedge M \cong M \oplus \Sigma M$. Is this a general ...
5 votes
1 answer
579 views

Topological Hochschild homology using equivariant orthogonal spectra

In the Hesselholt-Madsen paper "On the K-theory of finite algebras over Witt vectors of perfect fields", the authors develop some results concerning the Topological Hochschild homology (THH) of ...
6 votes
2 answers
1k views

Ring structures on algebraic K-theory spectrum, and its non-connective counterpart

I have a few naive questions on the algebraic K-theory spectrum construction, but whose answers I couldn't figure out using the internet. I'm mostly interested in the case of a commutative ring, but I ...
7 votes
2 answers
862 views

Detection of stable homotopy by K-theory spectra

This is primarily a reference request. Does anyone know of any writing about algebraic K-theory spectra picking up elements in the stable homotopy groups of spheres in their Hurewicz image coming from ...
5 votes
0 answers
178 views

Analytic refinement of generalized cohomology theories

Recently, U.Bunke and others developed in a number of papers (such as this, this or this) an approach to smooth extensions of cohomology theories based on stable homotopy theory. In this approach a ...
9 votes
1 answer
711 views

K-theory of the h-cobordism category

I was reading through Kervaire and Milnor's "Groups of Homotopy Spheres", in which the authors begin to compute the groups $\Theta_n$ of h-cobordism classes of homotopy $n$-spheres (with group ...