Homology, Homotopy and Applications

Volume 18 (2016)

Number 1

Higher Euler characteristics: Variations on a theme of Euler

Pages: 231 – 246

DOI: https://dx.doi.org/10.4310/HHA.2016.v18.n1.a12


Niranjan Ramachandran (Department of Mathematics, University of Maryland, College Park, Md., U.S.A.)


We provide a natural interpretation of the secondary Euler characteristic and introduce higher Euler characteristics. For a compact oriented manifold of odd dimension, the secondary Euler characteristic recovers the Kervaire semi-characteristic. We prove basic properties of the higher invariants and illustrate their use. We also introduce motivic variants.


Euler characteristic, abelian category, cohomological invariant

2010 Mathematics Subject Classification

13D15, 18G35, 55M99

Published 31 May 2016