All Questions
7 questions
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 ...
- 103
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 ...
- 63.9k
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 ...
- 254
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 ...
- 2,044
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 ...
- 912
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 ...
- 889
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 ...
- 10.4k