Classifying Spaces of Compact Lie Groups and Finite Loop Spaces

Notbohm, Dietrich

doi:10.1016/b978-044481779-2/50022-5

Cited by 27 publications

(21 citation statements)

References 51 publications

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“…We study these polynomial p-compact groups in this section. See also D. Notbohm [72,76,79] for further information and for references to the literature about this classical subject.…”

Section: 19mentioning

confidence: 99%

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N-determined p-compact groups

Møller

2002

Fund. Math.

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Abstract. One of the major problems in the homotopy theory of finite loop spaces is the classification problem for p-compact groups. It has been proposed to use the maximal torus normalizer (which at an odd prime essentially means the Weyl group) as the distinguishing invariant. We show here that the maximal torus normalizer does indeed classify many p-compact groups up to isomorphism when p is an odd prime.

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“…We study these polynomial p-compact groups in this section. See also D. Notbohm [72,76,79] for further information and for references to the literature about this classical subject.…”

Section: 19mentioning

confidence: 99%

“…It has been conjectured [53,72,26], in analogy with the classification theorem for compact Lie groups [25,83], that p-compact groups are determined by their maximal torus normalizers. The maximal torus normalizer N (X) for the p-compact group X is an extension…”

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confidence: 99%

N-determined p-compact groups

Møller

2002

Fund. Math.

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“…A p-compact toral group P is a p-compact group P such that π 0 (P ) ∼ = π 1 (BP ) is a finite p-group and such that the universal cover of BP is equivalent to an Eilenberg-MacLane space of the form K(Z ∧ p n , 2). For details and further notions we refer the reader to the above mentioned references and/or to the survey articles [5], [19] and [24].…”

Section: Particular Subgroups Of P-compact Groupsmentioning

confidence: 99%

The finiteness obstruction for loop spaces

Notbohm¹

1999

Commentarii Mathematici Helvetici

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Abstract. For finitely dominated spaces, Wall constructed a finiteness obstruction, which decides whether a space is equivalent to a finite CW -complex or not. It was conjectured that this finiteness obstruction always vanishes for quasi finite H-spaces, that are H-spaces whose homology looks like the homology of a finite CW -complex. In this paper we prove this conjecture for loop spaces. In particular, this shows that every quasi finite loop space is actually homotopy equivalent to a finite CW -complex. Mathematics Subject Classification (1991). 57Q12, 55R35, 55R10

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“…The normalizer ofT is the discrete approximation in the sense of [12, 3.12] to the normalizer of T [11, 9.8] (Aside 9.1). We take for granted the basic properties of 2-compact groups (see for instance the survey articles [20,22,26]), although we sometimes recall the definitions to help orient the reader. Since we only work with p-compact groups for p = 2, we sometimes abbreviate 2-complete to complete and 2-discrete to discrete.…”

Section: Propositionmentioning

confidence: 99%