All Questions

Is there a version of Noether's formula for the Euler characteristic of a surface for Real algebraic surfaces? Specifically, given $X$ a real algebraic compact smooth surface, what is the relationship ...

Let $p:B\to BO$ be a fibration. We say that a manifold has a $B$-structure if its stable tangent bundle lifts to $B$. I am interested in the question of whether there exists, for a given even ...

Edit: According to the interesting comments of Michael Albanese and Nick L we revise the question as follows: By manifold compactification of a manifold $M$ we mean a compact manifold $\tilde{M}$ ...

Are there simple necessary and sufficient conditions for an (oriented) even-dimensional compact smooth manifold to fiber over an (oriented) odd-dimensional manifold (with oriented fibers)? For ...