## Bikram Banerjee

*Chern rank of complex bundle*

Comment.Math.Univ.Carolin. 60,3 (2019) 401-413.**Abstract:**Motivated by the work of A.\,C.\ Naolekar and A.\,S.\ Thakur (2014) we introduce notions of upper chern rank and even cup length of a finite connected CW-complex and prove that upper chern rank is a homotopy invariant. It turns out that determination of upper chern rank 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 upper chern rank equal to its dimension, we provide a method of computing its even cup length. Finally, we compute upper chern rank of many interesting spaces.

**Keywords:** Chern class; characteristic rank; cup length; chern rank

**DOI:** DOI 10.14712/1213-7243.2019.015

**AMS Subject Classification:** 57R20

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