Cohomology of classifying spaces of central quotients of rank two Kac-Moody groups

Aguadé, Jaume; Broto, Carles; Kitchloo, Nitu; Saümell, Laia

doi:10.1215/kjm/1250281970

Cited by 11 publications

(29 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[27,16]). In particular, compare Theorem 1.1(ii) with Nitu Kitchloo's theorem to the e ect that the classifying space of a rank 2 Kac-Moody group of indeÿnite type is the homotopy pushout of a diagram of compact subgroups [16,Theorem 4.2.3] (see also [3,5]). …”

Section: Introductionmentioning

confidence: 99%

Homotopy decomposition of a group of symplectomorphisms of S2×S2

Anjos¹,

Granja²

2004

Topology

View full text Add to dashboard Cite

We continue the analysis started by Abreu, McDu and Anjos of the topology of the group of symplectomorphisms of S 2 × S 2 when the ratio of the area of the two spheres lies in the interval (1; 2]. We express the group, up to homotopy, as the pushout (or amalgam) of certain of its compact Lie subgroups. We use this to compute the homotopy type of the classifying space of the group of symplectomorphisms and the corresponding ring of characteristic classes for symplectic ÿbrations. ?

show abstract

Section: Introductionmentioning

confidence: 99%

Homotopy decomposition of a group of symplectomorphisms of S2×S2

Anjos¹,

Granja²

2004

Topology

View full text Add to dashboard Cite

show abstract

“…The determination of H * ((BG I ∧ q ) hψ k , F q ) for I ∈ S will occur in 5.2; this subsection will investigate H * ((BK ∧ q ) hψ k , F q ). In the simply connected rank 2 case, we have [3,33]…”

Section: 1mentioning

confidence: 99%

“…x 2l ] and H 2 * +1 (BK, F q ) = x 2l+1 H 2 * (BK, F q ) for x 2l+1 the image of a homogeneous degree 2l class under the connecting homomorphism [3]. The k th unstable Adams operation ψ k acts on H * (BT, F q ) via multiplication by p k on generators, and commutes with the restriction (45) H * (BG I , F q ) → H * (BT, F q ) [46].…”

Section: 1mentioning

confidence: 99%

“…within the proof of Theorem E. The methods of [3], where (48) is used to compute H * (BK, F q ), and a good understanding of the derivation associated to a twisted loop space should in principle allow further computation in the p k = 1(mod q) case. We preform no such calculations here but note that [5,Theorem 8.3] computes H * (BK(F p k ), F q ) in most of these interesting cases.…”

Section: 2mentioning

confidence: 99%

See 1 more Smart Citation

Discrete approximations for complex Kac–Moody groups

Foley

2015

Advances in Mathematics

View full text Add to dashboard Cite

Abstract. We construct a map from the classifying space of a discrete KacMoody group over the algebraic closure of the field with p elements to the classifying space of a complex topological Kac-Moody group and prove that it is a homology equivalence at primes q different from p. This generalises a classical result of Quillen-Friedlander-Mislin for Lie groups. As an application, we construct unstable Adams operations for general Kac-Moody groups compatible with the Frobenius homomorphism. Our results rely on new integral homology decompositions for certain infinite dimensional unipotent subgroups of discrete Kac-Moody groups.

show abstract

“…We are interested in these representations and in their rings of invariants. The mod p reductions of the representations of an infinite dihedral group in GL 2 (Z p ) were studied in [ABKS05] (see Table 1 in [ABKS05]). Let us summarize the results of [ABKS05] that we need here.…”

Section: The Weyl Group and Its Invariantsmentioning

confidence: 99%