**Title:** H-\infty Orientations and p-Typicality

**Speaker:** Justin Noel

**Speaker Info:** U of Chicago

**Brief Description:**

**Special Note**:

**Abstract:**

I will discuss recent work with Niles Johnson in which we show that at the primes 2 and 3, BP is not a commutative MU-algebra. More specifically, we show that there are no H_\infty complex orientations on BP.To keep the talk accessible, I will define H_\infty and E_\infty ring spectra and discuss their distinctions. I will also say a few words about BP.

Since the notion of an H_\infty ring spectrum is defined in the stable homotopy category, determining whether or not there is an H_\infty orientation is equivalent to an algebraic condition. Moreover, we can use the universal properties of BP to see that if the standard orientation isn't H_\infty, then there are no H_\infty orientations.

In the case of the standard orientation, McClure has already given the algebraic condition. This condition is moderately difficult to state and extremely difficult to compute. With great patience one can deduce the statement for p=2 by hand, but the condition at the prime 3 requires the aid of a computer.

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