Splitting of gauge groups

Daisuke Kishimoto; Akira Kono

doi:10.1090/S0002-9947-2010-05207-9

Splitting of gauge groups

Daisuke Kishimoto, Akira Kono

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

Let G be a topological group and let P be a principal G-bundle over a based space B. We denote the gauge group of P by G(P) and the based gauge group of P by G₀(P). Then the inclusion of the basepoint of B induces the exact sequence of topological groups 1 → G₀(P) → G(P) → G → 1. We study the splitting of this exact sequence in the category of A_n-spaces and An-maps in connection with the triviality of the adjoint bundle of P and with the higher homotopy commutativity of G.

Original language	English
Pages (from-to)	6715-6731
Number of pages	17
Journal	Transactions of the American Mathematical Society
Volume	362
Issue number	12
DOIs	https://doi.org/10.1090/S0002-9947-2010-05207-9
Publication status	Published - Dec 2010
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9947-2010-05207-9

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AU - Kishimoto, Daisuke

AU - Kono, Akira

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N2 - Let G be a topological group and let P be a principal G-bundle over a based space B. We denote the gauge group of P by G(P) and the based gauge group of P by G0(P). Then the inclusion of the basepoint of B induces the exact sequence of topological groups 1 → G0(P) → G(P) → G → 1. We study the splitting of this exact sequence in the category of An-spaces and An-maps in connection with the triviality of the adjoint bundle of P and with the higher homotopy commutativity of G.

AB - Let G be a topological group and let P be a principal G-bundle over a based space B. We denote the gauge group of P by G(P) and the based gauge group of P by G0(P). Then the inclusion of the basepoint of B induces the exact sequence of topological groups 1 → G0(P) → G(P) → G → 1. We study the splitting of this exact sequence in the category of An-spaces and An-maps in connection with the triviality of the adjoint bundle of P and with the higher homotopy commutativity of G.

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 12

ER -

Splitting of gauge groups

Abstract

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