BP: Close encounters of the E-infinity kind
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Mon, 17/10/2011 15:45 |
Andrew Baker (Glasgow) |
Topology Seminar  |
L3 |
| The notion of an E-infinity ring spectrum arose about thirty years ago, and was studied in depth by Peter May et al, then later reinterpreted in the framework of EKMM as equivalent to that of a commutative S-algebra. A great deal of work on the existence of E-infinity structures using various obstruction theories has led to a considerable enlargement of the body of known examples. Despite this, there are some gaps in our knowledge. The question that is a major motivation for this talk is `Does the Brown-Peterson spectrum BP for a prime p admit an E-infinity ring structure?'. This has been an important outstanding problem for almost four decades, despite various attempts to answer it. I will explain what BP is and give a brief history of the above problem. Then I will discuss a construction that gives a new E-infinity ring spectrum which agrees with BP if the latter has an E-infinity structure. However, I do not know how to prove this without assuming such a structure! | |||