Amenable groups and Euler characteristic (Q1195943)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Amenable groups and Euler characteristic |
scientific article; zbMATH DE number 86169
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Amenable groups and Euler characteristic |
scientific article; zbMATH DE number 86169 |
Statements
Amenable groups and Euler characteristic (English)
0 references
11 January 1993
0 references
Let \(G\) be an infinite amenable group and \(Y\) be a free cocompact \(G\)- space. The author shows that the Euler characteristic \(\chi(Y/G)\) has some special properties due to the amenability of \(G\). So, if \(H_ iY=0\) for \(0<i<m=\) dimension of \(Y\), then \((-1)^ m\chi(Y/G)\geq 0\) and \(=0\) only when \(H_ mY=0\). Some corollaries of this result are also obtained.
0 references
cell-complex
0 references
4-manifold
0 references
amenable group
0 references
Euler characteristic
0 references
