TY - JOUR
T1 - Homotopy pullback of An-spaces and its applications to An-types of gauge groups
AU - Tsutaya, Mitsunobu
N1 - Funding Information:
The author would like to express his gratitude to Professors Norio Iwase, Daisuke Kishimoto and Akira Kono for giving valuable comments on this work. This work was partially supported by Grant-in-Aid for JSPS Fellows Number 10J01265 .
Publisher Copyright:
© 2015 Elsevier B.V.
PY - 2015/6/1
Y1 - 2015/6/1
N2 - We construct the homotopy pullback of An-spaces and show some universal property of it. As the first application, we review Zabrodsky's result which states that for each prime p, there is a finite CW complex which admits an Ap-1-form but no Ap-form. As the second application, we investigate An-types of gauge groups. In particular, we give a new result on An-types of the gauge groups of principal SU(2)-bundles over S4, which is a complete classification when they are localized away from 2.
AB - We construct the homotopy pullback of An-spaces and show some universal property of it. As the first application, we review Zabrodsky's result which states that for each prime p, there is a finite CW complex which admits an Ap-1-form but no Ap-form. As the second application, we investigate An-types of gauge groups. In particular, we give a new result on An-types of the gauge groups of principal SU(2)-bundles over S4, which is a complete classification when they are localized away from 2.
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U2 - 10.1016/j.topol.2015.02.014
DO - 10.1016/j.topol.2015.02.014
M3 - Article
AN - SCOPUS:84924529799
SN - 0166-8641
VL - 187
SP - 1
EP - 25
JO - Topology and its Applications
JF - Topology and its Applications
ER -