Mixing
Is a union of compatible fiber bundles a fiber bundle?
Let $eta_i:E_irightarrow B_i$ be fiber bundles, and let $f_i:eta_irightarroweta_{i+1}$ be maps of fiber bundles.
Assuming that the bundles maps $eta_i$ are maps of smooth compact manifolds, and that the maps $f_i$ are inclusions of regular submanifolds, is the union $bigcup_ieta_i$ of the fiber bundles a fiber bundle?
I'm struggling to find a trivializing open cover of the base space of $bigcup_ieta_i$, but I think that it should be possible.
fiber-bundles
asked Nov 20 '18 at 13:36
user09127
574
add a comment |
Let $eta_i:E_irightarrow B_i$ be fiber bundles, and let $f_i:eta_irightarroweta_{i+1}$ be maps of fiber bundles.
Assuming that the bundles maps $eta_i$ are maps of smooth compact manifolds, and that the maps $f_i$ are inclusions of regular submanifolds, is the union $bigcup_ieta_i$ of the fiber bundles a fiber bundle?
I'm struggling to find a trivializing open cover of the base space of $bigcup_ieta_i$, but I think that it should be possible.
fiber-bundles
asked Nov 20 '18 at 13:36
user09127
574
add a comment |
Let $eta_i:E_irightarrow B_i$ be fiber bundles, and let $f_i:eta_irightarroweta_{i+1}$ be maps of fiber bundles.
Assuming that the bundles maps $eta_i$ are maps of smooth compact manifolds, and that the maps $f_i$ are inclusions of regular submanifolds, is the union $bigcup_ieta_i$ of the fiber bundles a fiber bundle?
I'm struggling to find a trivializing open cover of the base space of $bigcup_ieta_i$, but I think that it should be possible.
fiber-bundles
asked Nov 20 '18 at 13:36
user09127
574
Let $eta_i:E_irightarrow B_i$ be fiber bundles, and let $f_i:eta_irightarroweta_{i+1}$ be maps of fiber bundles.
Assuming that the bundles maps $eta_i$ are maps of smooth compact manifolds, and that the maps $f_i$ are inclusions of regular submanifolds, is the union $bigcup_ieta_i$ of the fiber bundles a fiber bundle?
I'm struggling to find a trivializing open cover of the base space of $bigcup_ieta_i$, but I think that it should be possible.
fiber-bundles
fiber-bundles
asked Nov 20 '18 at 13:36
user09127
574
asked Nov 20 '18 at 13:36
user09127
574
asked Nov 20 '18 at 13:36
user09127
574
asked Nov 20 '18 at 13:36
user09127
574
asked Nov 20 '18 at 13:36
user09127
574
574
add a comment |
add a comment |
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