Lefschetz formula for locally symmetric spaces

Yanli Song

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arXiv · 2502.16100

Lefschetz formula for locally symmetric spaces

Yanli Song

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Abstract

Let $G$ be a semi-simple real Lie group of real rank one and $\Gamma$ be a discrete subgroup in $G$ such that $\Gamma \backslash G$ has finite volume. We introduce a new group $C^*$-algebra $C^*_r(G, \Gamma)$, which provides a natural framework for defining index classes of Dirac-type operators on the locally symmetirc space $\Gamma \backslash G /K$. We show that Dirac operators define elements in the $K$-theory of $C^*_r(G, \Gamma)$ and use Hecke correspondences to study their Lefschetz numbers. Our main result is an explicit formula for the Lefschetz number of Hecke operators.

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BibTeX RIS

Yanli Song. 2025-02-22. Lefschetz formula for locally symmetric spaces. https://arxiv.org/abs/2502.16100

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