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Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).

10 votes
3 answers
2k views

Is the composition of two bundle projections necessarily a bundle projection?

That is, if $f: X \rightarrow Y$ and $g:Y \rightarrow Z$ are bundle projections, is $g \circ f: X \rightarrow Z$ a bundle projection? Assume $X$, $Y$ and $Z$ are manifolds. Here is what I know. The a …
Michael's user avatar
  • 143
4 votes
1 answer
658 views

composition of covering map and bundle projection

Hello, can somebody help with the following question that I have thought over for quite some time, to no avail? Suppose f: X--->Y is a universal cover and g: Y--->Z a fiber bundle, where X, Y and Z a …
Michael's user avatar
  • 143