Abstract
AbstractWe examine the relation between the gauge groups of $$\mathrm {SU}(n)$$
SU
(
n
)
- and $$\mathrm {PU}(n)$$
PU
(
n
)
-bundles over $$S^{2i}$$
S
2
i
, with $$2\le i\le n$$
2
≤
i
≤
n
, particularly when n is a prime. As special cases, for $$\mathrm {PU}(5)$$
PU
(
5
)
-bundles over $$S^4$$
S
4
, we show that there is a rational or p-local equivalence $$\mathcal {G}_{2,k}\simeq _{(p)}\mathcal {G}_{2,l}$$
G
2
,
k
≃
(
p
)
G
2
,
l
for any prime p if, and only if, $$(120,k)=(120,l)$$
(
120
,
k
)
=
(
120
,
l
)
, while for $$\mathrm {PU}(3)$$
PU
(
3
)
-bundles over $$S^6$$
S
6
there is an integral equivalence $$\mathcal {G}_{3,k}\simeq \mathcal {G}_{3,l}$$
G
3
,
k
≃
G
3
,
l
if, and only if, $$(120,k)=(120,l)$$
(
120
,
k
)
=
(
120
,
l
)
.
Publisher
Springer Science and Business Media LLC
Subject
Geometry and Topology,Algebra and Number Theory
Cited by
3 articles.
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