Homology, Homotopy and Applications

Volume 18 (2016)

Number 1

Higher Euler characteristics: Variations on a theme of Euler

Pages: 231 – 246

DOI: http://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

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