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VORONOI COMPLEXES IN HIGHER DIMENSIONS, COHOMOLOGY OF $GL_N (Z)$ FOR $N\ge 8$ AND THE TRIVIALITY OF $K_8 (Z)$
| hal.structure.identifier | Rudjer Boskovic Institute [Zagreb] | |
| dc.contributor.author | DUTOUR SIKIRIC, Mathieu | |
| hal.structure.identifier | Institut Fourier [IF ] | |
| dc.contributor.author | ELBAZ-VINCENT, Philippe | |
| hal.structure.identifier | Department of Mathematics [Cambridge] [HARVARD] | |
| dc.contributor.author | KUPERS, Alexander | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | MARTINET, Jacques | |
| dc.date.accessioned | 2024-04-04T02:59:24Z | |
| dc.date.available | 2024-04-04T02:59:24Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192740 | |
| dc.description.abstractEn | We enumerate the low dimensional cells in the Voronoi cell complexes attached to the modular groups $SL_N (Z)$ and $GL_N (Z)$ for $N = 8, 9, 10, 11$, using quotient sublattices techniques for $N = 8, 9$ and linear programming methods for higher dimensions. These enumerations allow us to compute some cohomology of these groups and prove that $K_8 (Z) = 0$, providing new knowledge on the Kummer-Vandiver conjecture. | |
| dc.description.sponsorship | IDEX UGA - ANR-15-IDEX-0002 | |
| dc.language.iso | en | |
| dc.subject.en | modular groups | |
| dc.subject.en | group cohomology | |
| dc.subject.en | Voronoi complex | |
| dc.subject.en | Perfect forms | |
| dc.subject.en | K-theory of integers | |
| dc.subject.en | well-rounded lattices | |
| dc.subject.en | Steinberg modules | |
| dc.subject.en | linear programming | |
| dc.subject.en | arithmetic groups | |
| dc.subject.en | Kummer-Vandiver conjecture | |
| dc.title.en | VORONOI COMPLEXES IN HIGHER DIMENSIONS, COHOMOLOGY OF $GL_N (Z)$ FOR $N\ge 8$ AND THE TRIVIALITY OF $K_8 (Z)$ | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.subject.hal | Mathématiques [math]/K-théorie et homologie [math.KT] | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-02333135 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02333135v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=DUTOUR%20SIKIRIC,%20Mathieu&ELBAZ-VINCENT,%20Philippe&KUPERS,%20Alexander&MARTINET,%20Jacques&rft.genre=preprint |
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