9
votes
2answers
383 views
When does an even-dimensional manifold fiber over an odd-dimensional manifold?
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 …
12
votes
1answer
318 views
Chern numbers via Euler characteristics?
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 …
6
votes
2answers
356 views
Top chern class under finite, unramified, dominant morphism
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 $ …
6
votes
0answers
78 views
“Mathai-Quillen-type” form on $M\times M$?
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 …
0
votes
0answers
77 views
Euler characteristic of homology theory of one object divides that of another
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?
3
votes
1answer
184 views
Euler characteristics and the difference bundle construction
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 …
14
votes
3answers
722 views
Is Euler characteristic of a simplicial complex upper bounded by a polynomial in the number of its facets ?
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 …
2
votes
1answer
239 views
Higher Euler characteristics (possible generalizations)
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 …
7
votes
2answers
438 views
Is the Euler characteristic of aspherical connected 2-complexes at most 1? (No!) What can be said about subcomplexes of 2-complexes deformation retractible onto graphs.
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 …
0
votes
2answers
224 views
The query concerning the Euler-Poincare formula’s generalizations
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. …
0
votes
0answers
69 views
Converting global coordinates into set of local matrices for ik skeleton creation
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 …
6
votes
1answer
336 views
Multiplicativity of Euler characteristic for non-orientable fibrations
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 …
3
votes
1answer
160 views
non degenerate quadratic form on the group of correspondences on an algebraic curve?
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 …
12
votes
2answers
879 views
Spaces that are both homotopically and cohomologically finite
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 …
7
votes
0answers
466 views
Euler Characteristic of a Variety
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 …

