Lefschetz formula for locally symmetric spaces
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916867663200256 |
|---|---|
| author | Song, Yanli |
| author_facet | Song, Yanli |
| contents | Let $G$ be a semi-simple real Lie group of real rank one and $Γ$ be a discrete subgroup in $G$ such that $Γ\backslash G$ has finite volume. We introduce a new group $C^*$-algebra $C^*_r(G, Γ)$, which provides a natural framework for defining index classes of Dirac-type operators on the locally symmetirc space $Γ\backslash G /K$. We show that Dirac operators define elements in the $K$-theory of $C^*_r(G, Γ)$ and use Hecke correspondences to study their Lefschetz numbers. Our main result is an explicit formula for the Lefschetz number of Hecke operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16100 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lefschetz formula for locally symmetric spaces Song, Yanli K-Theory and Homology Differential Geometry Number Theory Representation Theory 11F72, 58B34, 19K56, 19K35, 58J20 Let $G$ be a semi-simple real Lie group of real rank one and $Γ$ be a discrete subgroup in $G$ such that $Γ\backslash G$ has finite volume. We introduce a new group $C^*$-algebra $C^*_r(G, Γ)$, which provides a natural framework for defining index classes of Dirac-type operators on the locally symmetirc space $Γ\backslash G /K$. We show that Dirac operators define elements in the $K$-theory of $C^*_r(G, Γ)$ and use Hecke correspondences to study their Lefschetz numbers. Our main result is an explicit formula for the Lefschetz number of Hecke operators. |
| title | Lefschetz formula for locally symmetric spaces |
| topic | K-Theory and Homology Differential Geometry Number Theory Representation Theory 11F72, 58B34, 19K56, 19K35, 58J20 |
| url | https://arxiv.org/abs/2502.16100 |