Discrete approximations for complex Kac–Moody groups

Foley, John D.

doi:10.1016/j.aim.2014.09.015

Cited by 3 publications

(2 citation statements)

References 39 publications

(115 reference statements)

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“…If we assume that all compositions ge n are null, then any g is null by applying [40, Lemma 6.2] to BX I . Moreover, the identification (17) implies that • g is null if and only g is null and…”

Section: Maps From P-compact Toral Groupsmentioning

confidence: 99%

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Recognizing nullhomotopic maps into the classifying space of a Kac-Moody group

Foley

2015

Preprint

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This paper extends certain characterizations of nullhomotopic maps between p-compact groups to maps with target the p-completed classifying space of a connected Kac-Moody group and source the classifying space of either a p-compact group or a connected Kac-Moody group. A well known inductive principle for p-compact groups is applied to obtain general, mapping space level results. An arithmetic fiber square computation shows that a null map from the classifying space of a connected compact Lie group to the classifying space of a connected topological Kac-Moody group can be detected by restricting to the maximal torus. Null maps between the classifying spaces of connected topological Kac-Moody groups cannot, in general, be detected by restricting to the maximal torus due to the nonvanishing of an explicit abelian group of obstructions described here. Nevertheless, partial results are obtained via the application of algebraic discrete Morse theory to higher derived limit calculations which show that such detection is possible in many cases of interest.

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Section: Maps From P-compact Toral Groupsmentioning

confidence: 99%

“…[27,Theorem 1] and [2, § 10]). Though unstable Adams operations for Kac-Moody groups have been constructed, their homotopical uniqueness is not settled for rank greater than 2 [17,Theorem D and Question 4.4]).…”

Section: Introductionmentioning

confidence: 99%

Recognizing nullhomotopic maps into the classifying space of a Kac-Moody group

Foley

2015

Preprint

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Recognizing nullhomotopic maps into the classifying space of a Kac–Moody group

Foley¹

2022

Math. Z.

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On some applications of unstable Adams operations to the topology of Kac-Moody groups

Kitchloo

2016

Proc. Amer. Math. Soc.

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ABSTRACT. Localized at almost all primes, we describe the structure of differentials in several important spectral sequences that compute the cohomology of classifying spaces of topological Kac-Moody groups. In particular, we show that for all but a finite set of primes, these spectral sequences collapse and that there are no additive extension problems. We also describe some appealing consequences of these results. The main tool is the use of the naturality properties of unstable Adams operations on these classifying spaces.

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Discrete approximations for complex Kac–Moody groups

Cited by 3 publications

References 39 publications

Recognizing nullhomotopic maps into the classifying space of a Kac-Moody group

Recognizing nullhomotopic maps into the classifying space of a Kac-Moody group

Recognizing nullhomotopic maps into the classifying space of a Kac–Moody group

On some applications of unstable Adams operations to the topology of Kac-Moody groups

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