Locally symmetric spaces and K-theory of number fields

For a closed locally symmetric space M=\Gamma\G/K and a representation of G we consider the push-forward of the fundamental class in the homology of the linear group and a related invariant in algebraic K-theory. We discuss the nontriviality of this invariant and we generalize the construction to cusped locally symmetric spaces of R-rank one.

💡 Research Summary

The paper investigates a bridge between the geometry of locally symmetric spaces and the algebraic K‑theory of number fields. Starting with a closed locally symmetric manifold (M=\Gamma\backslash G/K), where (G) is a semisimple real Lie group, (K) a maximal compact subgroup, and (\Gamma) an arithmetic lattice, the authors consider a finite‑dimensional linear representation (\rho\colon G\to GL_N(\mathbb C)). The fundamental class (