Chern Rank of Complex Bundle
Algebraic Topology
2018-01-24 v2
Abstract
We introduce notions of {\it upper chernrank} and {\it even cup length} of a finite connected CW-complex and prove that {\it upper chernrank} is a homotopy invariant. It turns out that determination of {\it upper chernrank} of a space sometimes helps to detect whether a generator of the top cohomology group can be realized as Euler class for some real (orientable) vector bundle over or not. For a closed connected -dimensional complex manifold we obtain an upper bound of its even cup length. For a finite connected even dimensional CW-complex with its {\it upper chernrank} equal to its dimension, we provide a method of computing its even cup length. Finally, we compute {\it upper chernrank} of many interesting spaces.
Cite
@article{arxiv.1708.05871,
title = {Chern Rank of Complex Bundle},
author = {Bikram Banerjee},
journal= {arXiv preprint arXiv:1708.05871},
year = {2018}
}