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23 votes
6 answers
2k views

Is there a topological description of combinatorial Euler characteristic?

There are a collection of definitions of "combinatorial Euler characteristic", which is different from the "homotopy Euler characteristic". I will describe a few of them and give some references, and …
5 votes
1 answer
687 views

What is the Euler characteristic of a mapping space?

Suppose that $A$ and $B$ are topological spaces homotopy equivalent to finite cell complexes, and let $B^A = \mathrm{maps}(A,B)$ denote the space of maps from $A$ to $B$. Is it there a formula for th …
10 votes
2 answers
700 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 oriented fibers)? For ex …
4 votes
1 answer
894 views

"Wick rotation" of tropical geometry

This question is related to my earlier, even more open-ended question on tropilcalization. I will give some background and ask my question at the end. On R, consider the family of commutative, assoc …