Euler characteristics of arithmetic groups
| dc.creator | Horozov, Ivan E. | |
| dc.date | 2003-11-07 | |
| dc.date.accessioned | 2026-07-07T05:02:43Z | |
| dc.date.available | 2026-07-07T05:02:43Z | |
| dc.description | We develop a general method for computing the homological Euler characteristic of finite index subgroups G of GL_m(O_K) where O_K is the ring of integers in a number field K. With this method we find, that for large, explicitly computed dimensions m, the homological Euler characteristic of finite index subgroups of GL_m(O_K) vanishes. For other cases, some of them very important for spaces of multiple polylogarithms, we compute non-zero homological Euler characteristic. With the same method we find all the torsion elements in GL_3(Z) up to conjugation. Finally, our method allows us to obtain a formula for the Dedekind zeta function at -1 in terms of the ideal class set and the multiplicative group of quadratic extensions of the base ring. | |
| dc.description | LaTeX, 94 pages | |
| dc.identifier | https://arxiv.org/abs/math/0311117 | |
| dc.identifier | http://arxiv.org/abs/math/0311117 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69119 | |
| dc.subject | Group Theory | |
| dc.subject | 20G10 | |
| dc.title | Euler characteristics of arithmetic groups | |
| dc.type | text |