Results 1 
7 of
7
THOM PROSPECTRA FOR LOOPGROUP REPRESENTATIONS
"... Abstract. This is very much an account of work in progress. We sketch the construction of an Atiyah dual (in the category of Tspaces) for the free loopspace of a manifold; the main technical tool is a kind of Tits building for loop groups, discussed in detail in an appendix. Together with a new loc ..."
Abstract

Cited by 10 (2 self)
 Add to MetaCart
(Show Context)
Abstract. This is very much an account of work in progress. We sketch the construction of an Atiyah dual (in the category of Tspaces) for the free loopspace of a manifold; the main technical tool is a kind of Tits building for loop groups, discussed in detail in an appendix. Together with a new localization theorem for Tequivariant Ktheory, this yields a construction of the elliptic genus in the string topology framework of ChasSullivan, CohenJones, Dwyer, Klein, and others. We also show how the Tits building can be used to construct the dualizing spectrum of the loop group. Using a tentative notion of equivariant Ktheory for loop groups, we relate the equivariant Ktheory of the dualizing spectrum to recent work of Freed, Hopkins and Teleman.
TOWARD A FUNDAMENTAL GROUPOID FOR THE STABLE HOMOTOPY CATEGORY
, 2005
"... Abstract. This very speculative talk suggests that a theory of fundamental groupoids for tensor triangulated categories could be used to describe the ring of integers as the singular fiber in a family of ringspectra parametrized by a structure space for the stable homotopy category, and that Bousfi ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
Abstract. This very speculative talk suggests that a theory of fundamental groupoids for tensor triangulated categories could be used to describe the ring of integers as the singular fiber in a family of ringspectra parametrized by a structure space for the stable homotopy category, and that Bousfield localization might be part of a theory of ‘nearby ’ cycles for stacks or orbifolds. One of the motivations for this talk comes from John Rognes ’ Galois theory for structured ring spectra. His paper [37] ends with some very interesting remarks about analogies between classical primes in algebraic number fields and the nonEuclidean primes of the stable homotopy category, and I try here to develop a
Homotopy groups of homotopy fixed point spectra associated to En
 In Proceedings of the Nishida Fest, Kinosaki, 2003, in Geom. Topol. Monogr
, 2007
"... We compute the mod.p / homotopy groups of the continuous homotopy fixed point ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We compute the mod.p / homotopy groups of the continuous homotopy fixed point
Homotopy groups of homotopy fixed point spectra associated to
"... pagination and layout may vary from GTM published version ..."
Milnor operations and the generalized Chern character
, 2007
"... We have shown that the n–th Morava K –theory K ∗ (X) for a CW–spectrum X with action of Morava stabilizer group Gn can be recovered from the system of some height–(n + 1) cohomology groups E ∗ (Z) with Gn+1 –action indexed by finite subspectra Z. In this note we reformulate and extend the above res ..."
Abstract
 Add to MetaCart
We have shown that the n–th Morava K –theory K ∗ (X) for a CW–spectrum X with action of Morava stabilizer group Gn can be recovered from the system of some height–(n + 1) cohomology groups E ∗ (Z) with Gn+1 –action indexed by finite subspectra Z. In this note we reformulate and extend the above result. We construct a symmetric monoidal functor F from the category of E ∨ ∗ (E)–precomodules to the category of K∗(K)–comodules. Then we show that K ∗ (X) is naturally isomorphic to the inverse limit of F(E ∗ (Z)) as a K∗(K)–comodule.