Mathematical Sciences Geometry/Topology Seminar

April 29 (This is a Tuesday):
Speaker: Ivonne Ortiz (Binghamton)
Title: The lower algebraic K-theory of GAMMA_3

In this dissertation we compute the lower algebraic K-theory of $ \Gamma_3$ a discrete subgroup of the group of isometries of hyperbolic 3-space. This group forms part of a family of hyperbolic, non-cocompact, n-simplex reflection groups from which to study the problem of computing the K-theory of infinite groups with torsion. The main results for $ \Gamma_3$ are:

.....the Whitehead group of $ \Gamma_3$ is zero,

..... $ \tilde K_0({\bf Z}\Gamma_3) = {\bf Z}/4 \oplus \tilde K_0({\bf Z}[{\bf Z}/2 \times S_4])$,

...... $ K_{-1}({\bf Z}\Gamma_3) = {\bf Z}\oplus {\bf Z}$ and

...... $ K_n({\bf Z}\Gamma_3)$ is zero for all $ n < -1$.