# Tagged Questions

**4**

votes

**0**answers

165 views

### Which ring spectra have some kind of exponential map turning addition into multiplication?

This accepted answer to the question about $BU_\otimes$ made me recall that I want to read about this general phenomenon for a long time.
What will follow is sort of vernacular but whether it can be ...

**17**

votes

**0**answers

440 views

### Calabi-Yau cohomology?

My question here is going to be this -- but I'll give a bit of background to explain myself in a moment:
What has been done/what results are available on Calabi-Yau cohomology in degree $n \geq 3$ ...

**10**

votes

**0**answers

170 views

### “topological” Ochanine genus?

The Witten genus has famously been lifted to the string orientation of tmf ("topological Witten genus"). For the Ochanine genus I am aware of a lift to a "spin orientation of Tate K-theory", namely to ...

**16**

votes

**2**answers

578 views

### KK-theory as a stable infinity-category and KU Mod

The category KK of bivariant operator K-theory (or possibly its E-theory variant) ought to be the homotopy category of something at least close to a stable infinity-category; notably in that it ...

**3**

votes

**0**answers

150 views

### In the cohomology of Thom spectrum over LoopS^{2} and p-adic characteristic classes

Let $T$ denote the thom spectrum over $\Omega S^{2}$ defined by the map
$1+3: \Omega S^{2} \to BG_{3}$
where $1 +3$ is a unit in $3$-adics.
Here $G_{3}$ is the unit component of ...

**4**

votes

**1**answer

386 views

### Formal Group Laws on Ring Spectra?

Given a (graded) ring $R$, to define a formal group law it is equivalent to define a ring homomorphism $\phi:L\to R$ where $L$ is Lazard's ring. Is there any notion of defining a formal group law on ...

**25**

votes

**4**answers

1k views

### Integral cohomology (stable) operations

There have been a couple questions on MO, and elsewhere, that have made me curious about integral or rational cohomology operations. I feel pretty familiar with the classical Steenrod algebra and its ...

**15**

votes

**2**answers

1k views

### Is there a map of spectra implementing the Thom isomorphism?

A well known theorem in algebraic topology relates the (co)homology of the Thom space $X^\mu$ of a orientable vector bundle $\mu$ of dimension $n$ over a space $X$ to the (co)homology of $X$ itself: ...

**13**

votes

**1**answer

709 views

### Complex orientations on homotopy

I am wondering if there is a more "geometric" formulation of complex orientations for cohomology theories than just a computation of $E^*\mathbb{C}$P$^{\infty}$ or a statement about Thom classes. It ...

**8**

votes

**1**answer

377 views

### Are generalized cohomology theories a homotopy category of some category of invariants?

I was taught to think of generalized cohomology theories as the homotopy category of (symmetric) spectra. But is there also a category of 'invariants', that is, some category of contravariant functors ...