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