# Tagged Questions

**5**

votes

**1**answer

315 views

### Dennis trace map K----> THH

I have some questions about Dennis trace map in algebraic K-Theory. I was wondering if there is some conceptual way to look at this map $K(-)\rightarrow THH(-)$ (natural transformation from K-Theory ...

**23**

votes

**4**answers

1k views

### What (if anything) unifies stable homotopy theory and Grothendieck's six functors formalism?

I know of two very general frameworks for describing generalizations of what a "cohomology theory" should be: Grothendieck's "six functors", and the theory of spectra.
In the former, one assigns to ...

**2**

votes

**1**answer

141 views

### Is there a geometric interpretation of Johnson-Wilson E(n) analogous to vector bundles for K-theory?

I am reading Ravenel's Localization with Respect to Certain Periodic Homology Theories where he states;
For $n\ge2$, the spectra E(n)
represent periodic homology theories which at present have ...

**18**

votes

**0**answers

477 views

### What is to tmf as KR is to KO?

The $E_\infty$-ring spectrum $KU$ of complex K-theory carries a canonical involution induced from complex conjugation of complex vector bundles. The homotopy fixed points of this $\mathbb{Z}_2$-action ...

**16**

votes

**2**answers

504 views

### Conceptual explanation for the relationship between Clifford algebras and KO

Recall the following table of Clifford algebras:
$$\begin{array}{ccc}
n & Cl_n & M_n/i^{*}M_{n+1}\\
1 & \mathbb{C} & \mathbb{Z}/2\mathbb{Z} \\
2 & \mathbb{H} & ...

**33**

votes

**3**answers

843 views

### Lambda-operations on stable homotopy groups of spheres

The Barratt-Quillen-Priddy theorem says in one interpretation that there is a weak equivalence of spectra $K(FinSet) \simeq \mathbb{S}^0$. In other words K-theory groups of finite sets are the stable ...

**12**

votes

**2**answers

880 views

### Finiteness of stable homotopy groups of spheres

Since the work of Serre in the early 50's on homotopy groups of spheres, it is known that the homotopy group $\pi_k(S^n)$ is finite, except when $k=n$ (in which case the group is $\mathbb{Z}$), or ...