TY - JOUR
T1 - Higher homotopy commutativity in localized Lie groups and gauge groups
AU - Hasui, Sho
AU - Kishimoto, Daisuke
AU - Tsutaya, Mitsunobu
N1 - Funding Information:
M.T. is supported by a Grant for Scientific Research Projects from The Sumitomo Foundation and by JSPS KAKENHI (16K17592)
Publisher Copyright:
© 2018, International Press.
PY - 2019
Y1 - 2019
N2 - The first aim of this paper is to study the p-local higher homotopy commutativity of Lie groups in the sense of Sugawara. The second aim is to apply this result to the p-local higher homotopy commutativity of gauge groups. Although the higher homotopy commutativity of Lie groups in the sense of Williams is already known, the higher homotopy commutativity in the sense of Sugawara is necessary for this application. The third aim is to resolve the 5-local higher homotopy noncommutativity problem of the exceptional Lie group G2, which has been open for a long time.
AB - The first aim of this paper is to study the p-local higher homotopy commutativity of Lie groups in the sense of Sugawara. The second aim is to apply this result to the p-local higher homotopy commutativity of gauge groups. Although the higher homotopy commutativity of Lie groups in the sense of Williams is already known, the higher homotopy commutativity in the sense of Sugawara is necessary for this application. The third aim is to resolve the 5-local higher homotopy noncommutativity problem of the exceptional Lie group G2, which has been open for a long time.
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U2 - 10.4310/HHA.2019.v21.n1.a6
DO - 10.4310/HHA.2019.v21.n1.a6
M3 - Article
AN - SCOPUS:85057756600
SN - 1532-0073
VL - 21
SP - 107
EP - 128
JO - Homology, Homotopy and Applications
JF - Homology, Homotopy and Applications
IS - 1
ER -