Are there simple necessary and sufficient conditions for an (oriented) even-dimensional compact smooth manifold to fiber over an (oriented) odd-dimensional manifold (with orient …

Let $X$ be a space good enough to have a fundamental class, and $E$ a complex vector bundle on $X$. Let $P$ be some polynomial expression, and say I want to evaluate $P(c_i(E)) \c …

Situation: Let $\Bbbk$ be an algebraically closed field. Assume that $\pi:Y\to X$ is an finite, dominant, unramified morphism between nonsingular varieties of dimensions $n$. Let $ …

Let $(M,g)$ be a compact, oriented, $(2n)$-dimensional Riemannian manifold. I'm wondering whether there is a "canonical" construction of a $(2n)$-form $\eta_g$ on $M\times M$, suc …

Suppose we have a homology theory such that the associated Euler characteristic of one object divides that of another. What can we infer from this?

I am reading on K theory in Lawson and Michelson (Spin Geometry). One has the "exact sequence spaces" $L(X,Y)$ and there is the theorem that there is a unique equivalence of functo …

What is the best upper bound known on the (absolute value of) the Euler characteristic of a simplicial complex in terms of the number of its facets ? In particular, I am interest …

Let $X$ be projective and Gorenstein (over $\mathbb{C}$), of dimension $n$, then $\chi(\mathcal{O}_X)=(-1)^n\chi(w_X)$. Hence a "generalization": $\chi(w^{\otimes k}_X)$. I'd lik …

I have several related questions, i do not know which one is more important to me, i think it would depend on their answers. Is it true that the Euler characteristic of a finite …

Euler's equation for polyhedral, Euler's polyhedral formula, V – E + F = 2, where V, E, and F, are the number of points, edges and faces, was discovered by Leonhard Euler in 1752. …

I have the 3d global positions of a set of joints as they move over time and the ik skeleton structure which relates them. I am currently writing some code to convert this informat …

Let $E\to B$ be a fibration with fiber F, and assume for simplicity that B is connected. Suppose moreover that B and F have Euler characteristics (perhaps they are manifolds). Th …

Hi, Given two (smooth, projective) curves $X$ and $Y$ over a field $k$, define a correspondence to be a line bundle $L$ on $X\times Y$. A trivial correspondence is a correspondenc …

Is it true that every connected space with 1) just finitely many nontrivial homotopy groups, all finite, and 2) just finitely many nontrivial rational cohomology groups, all f …

Let $Y$ be a "nice" scheme. I am thinking projective varieties over an algebraically closed field, for now, but I am open to more general results. In terms of singular …