Realizing cohomology classes as Euler classes

Year, pages: 2012, 949 - 966

For a space $X$, let $E_k(X)$, $E_k^s(X)$ and $E^\circ_k(X)$ denote respectively the set of Euler classes of oriented $k$-plane bundles over $X$, the set of Euler classes of stably trivial $k$-plane bundles over $X$ and the spherical classes in $H^k(X;\mathbb Z)$. We prove some general facts about the sets $E_k(X)$, $E_k^s(X)$ and $E_k^\circ(X)$. We also compute these sets in the cases where $X$ is a projective space, the Dold manifold $P(m,1)$ and obtain partial computations in the case that $X$ is a product of spheres.

Naolekar, A. 2012. Realizing cohomology classes as Euler classes. In Mathematica Slovaca, vol. 62, no.5, pp. 949-966. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0057-2

Naolekar, A. (2012). Realizing cohomology classes as Euler classes. Mathematica Slovaca, 62(5), 949-966. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0057-2