Topological classification of generalized Bott towers

Details Topological classification of generalized Bott towers Topological classification of generalized Bott towers

2008-07-28

arxiv.org/abs/0807.4334v1

Trans. Amer. Math. Soc. 362 (2010), 1097--1112

Mathematics

Algebraic Topology

18 pages

Scientific paper

If $B$ is a toric manifold and $E$ is a Whitney sum of complex line bundles over $B$, then the projectivization $P(E)$ of $E$ is again a toric manifold. Starting with $B$ as a point and repeating this construction, we obtain a sequence of complex projective bundles which we call a generalized Bott tower. We prove that if the top manifold in the tower has the same cohomology ring as a product of complex projective spaces, then every fibration in the tower is trivial so that the top manifold is diffeomorphic to the product of complex projective spaces. This gives a supporting evidence to what we call cohomological rigidity problem for toric manifolds "Are toric manifolds diffeomorphic (or homeomorphic) if their cohomology rings are isomorphic?" We provide two more results which support the cohomological rigidity problem.

Affiliated with

Also associated with

No associations

Rating

Topological classification of generalized Bott towers does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Topological classification of generalized Bott towers, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Topological classification of generalized Bott towers will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-312576