Jul 2, 2024 · In fact once we know that orbifold Euler characteristic is well-behaved this calculation implies that the free subgroups of $\Gamma$ must have index divisible by $6$, so this is the largest …

Aug 14, 2016 · For other geometric interpretations of the Euler characteristic, you can just take a look at the wikipedia article, which for instance mentions links with homological invariants of vector bundles …

That a compact manifold M with vanishing Euler characteristic has a nonvanishing vector field was proved by Heinz Hopf, Vektorfelder in Mannifaltigkeiten, Math.

To deduce additivity of Euler characteristic you need to use also that all strata are even dimensional. For instance additivity fails for a point on the real line. The point being that the intersection of the two …

The reason is that the Euler characteristic is invariant of the projective embedding (it is a topological invariant), while the equations defining a variety are certainly not. For example, it is known that any …

Mar 22, 2022 · The morphism is the so called integration with respect to the Euler characteristic. For an informal introduction to this topic and some surprising applications I refer to this old seminar …

The Chern-MacPherson class computes the topological Euler characteristic of a (possibly singular) variety. -The Chern-Mather-class enters the definition of the Chern-MacPherson class. It is relevant …

Multiplicativity of Euler characteristic for non-orientable fibrations Ask Question Asked 14 years, 4 months ago Modified 7 years, 11 months ago

Jan 17, 2012 · Why is the Euler characteristic of a boundary even? How can one prove this and is there an geometric way to think about it?

May 10, 2020 · If one calculates the Euler characteristic by counting cells in a CW decomposition, the easiest one is to attach a 2-cell to a point to get a sphere. Then the number of 0-cells is 1, the …