All Questions
Tagged with euler-characteristics gn.general-topology
7 questions
3
votes
1
answer
539
views
Euler characteristic of pseudomanifolds with boundary
It is a well-known fact that for every compact oriented odd-dimensional manifold $\mathcal{M}$ with boundary it holds that
$$\chi(\mathcal{M})=\frac{1}{2}\chi(\partial\mathcal{M}).$$
In particular, if ...
- 1,429
7
votes
1
answer
500
views
Refined Euler characteristic
Is there a refinement of Euler characteristic that distinguishes between the torus $S^1 \times S^1$ and the cylinder $S^1 \times [0,1]$?
(The intuition here is that $\chi$ is multiplicative, so that $...
- 19.7k
7
votes
1
answer
615
views
Compactification of open manifolds in the form of a manifold( with zero Euler characteristic)
Edit: According to the interesting comments of Michael Albanese and Nick L we revise the question as follows:
By manifold compactification of a manifold $M$ we mean a compact manifold $\tilde{M}$ ...
- 366
4
votes
3
answers
1k
views
Morse theory and Euler characteristics
Suppose we have a space M with a real-valued, differentiable function F on M. Under what conditions on F will the Euler characteristic of M be expressed as a (signed) sum of Euler characteristics of ...
- 1,129
5
votes
2
answers
1k
views
Relating Euler characteristic, intersection product, Morse theory (plus SU(2) and 3-manifolds)
Suppose we have a (closed, oriented) 3-manifold M with a Heegard surface F of genus g. Let F* denote F with a puncture. Then the space H of representations of pi_1(F*) on SU(2) is just SU(2)^2g, and ...
- 1,129
11
votes
1
answer
336
views
cardinality of final coalgebras in Top
Let P be a polynomial functor from Top to Top, by which I mean a functor of the form P(X) = ∐i ≥ 0 Si × Xi where the Si are finite sets, all but finitely many of which are empty. ...
- 25.2k
23
votes
6
answers
2k
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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 ...
- 54.6k