A note on the characteristic rank and related numbers

2013/07/11 by L'udovít Balko, Balko, L'udovít, Július Korbaš +1
Mathematics · #57R20 05A17 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #Differential Geometry (math.DG) #FOS: Mathematics #Number Theory (math.NT) #math.AT #math.CO #math.DG #math.NT #msc:05A17 #msc:57R20

paper · pdf · doi:10.48550/arxiv.1307.3031

Accepted for publication in Mathematica Slovaca

arxiv created 2013/07/11 · arxiv updated 2013/07/12

Abstract

This note quantifies, via a sharp inequality, an interplay between (a) the characteristic rank of a vector bundle over a topological space X, (b) the Z/2Z-Betti numbers of X, and (c) sums of the numbers of certain partitions of integers. In a particular context, (c) is transformed into a sum of the readily calculable Betti numbers of the real Grassmann manifolds.

Related

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