Splitting of gauge groups

Kishimoto, Daisuke; Kono, Akira

doi:10.1090/s0002-9947-2010-05207-9

Cited by 14 publications

(19 citation statements)

References 25 publications

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“…Though the following proposition is partially proved in [KK10], we give another proof. Map(B n G, BG) → BG → BWA n (G, G; eq), the conditions (ii) and (iii) are equivalent.…”

Section: Application: a N -Types Of Gauge Groupsmentioning

confidence: 96%

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Mapping spaces from projective spaces

Tsutaya

2016

Homology, Homotopy and Applications

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Abstract. We denote the n-th projective space of a topological monoid G by B n G and the classifying space by BG. Let G be a well-pointed topological monoid having the homotopy type of a CW complex and G a well-pointed grouplike topological monoid. We prove that there is a natural weak equivalence between the pointed mapping space Map 0 (B n G, BG ) and the space A n (G, G ) of all A n -maps from G to G . Moreover, if we suppose G = G , then an appropriate union of path-components of Map 0 (B n G, BG) is delooped.This fact has several applications. As the first application, we show that the evaluation fiber sequence Map 0 (B n G, BG) → Map(B n G, BG) → BG extends to the right. As other applications, we investigate higher homotopy commutativity, A n -types of gauge groups, T

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“…Though the following proposition is partially proved in [KK10], we give another proof. Map(B n G, BG) → BG → BWA n (G, G; eq), the conditions (ii) and (iii) are equivalent.…”

Section: Application: a N -Types Of Gauge Groupsmentioning

confidence: 96%

“…Recall that they are described by using projective spaces as follows. See [Saü95] for the proof of (i), [KK10] for (ii), and [HK11] for (iii) and (iv). Obviously, any Sugawara C n -space is a C k (n)-space for k ≤ n, and any C k (n)-space is a C(k, n − k)-space.…”

Section: Application: Higher Homotopy Commutativitymentioning

confidence: 99%

Mapping spaces from projective spaces

Tsutaya

2016

Homology, Homotopy and Applications

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“…Hence φ is an isomorphism between modules of indecomposables, implying that φ is an isomorphism of unstable algebras. Thus the composite As in the proof of [KK,Theorem 1.2], the A n -triviality of (ad P α ) (p) implies that G (P α ) (p) and G (S d × G) (p) have the same A n -type. We show the converse under some conditions.…”

Section: Proof Of Theorem 11mentioning

confidence: 75%

Infiniteness ofA_∞-types of gauge groups

Kishimoto¹,

Tsutaya²

2015

J Topology

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Abstract. Let G be a compact connected Lie group and let P be a principal G-bundle over K. The gauge group of P is the topological group of automorphisms of P . For fixed G and K, consider all principal G-bundles P over K. It is proved in [CS, Ts] that the number of A n -types of the gauge groups of P is finite if n < ∞ and K is a finite complex. We show that the number of A ∞ -types of the gauge groups of P is infinite if K is a sphere and there are infinitely many P .

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“…In [10,12,13,19] and study their properties [11], nothing has been done for their classifying spaces.…”

Section: Introductionmentioning

confidence: 99%

Homotopy decompositions of the classifying spaces of pointed gauge groups

Theriault

2019

Pacific J. Math.

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Let G be a topological group and let G * (P) be the pointed gauge group of a principal G-bundle P −→ M. We prove that if G is homotopy commutative then the homotopy type of the classifying space BG * (P) can be completely determined for certain M. This also works p-locally, and valid choices of M include closed simply-connected four-manifolds when localized at an odd prime p. In this case, an application is to calculate part of the mod-p homology of the classifying space of the full gauge group.

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Splitting of gauge groups

Cited by 14 publications

References 25 publications

Mapping spaces from projective spaces

Mapping spaces from projective spaces

Infiniteness ofA_∞-types of gauge groups

Homotopy decompositions of the classifying spaces of pointed gauge groups

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Splitting of gauge groups

Cited by 14 publications

References 25 publications

Mapping spaces from projective spaces

Mapping spaces from projective spaces

Infiniteness ofA∞-types of gauge groups

Homotopy decompositions of the classifying spaces of pointed gauge groups

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Product

Resources

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Infiniteness ofA_∞-types of gauge groups