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 interested in proving or ...
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 connected aspherical ...