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arXiv · 1708.05871

Chern Rank of Complex Bundle

Bikram Banerjee
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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 $X$ 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 $X$ or not. For a closed connected $d$-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.

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Bikram Banerjee. 2017-08-19. Chern Rank of Complex Bundle. https://arxiv.org/abs/1708.05871

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