Consider representations \(\rho\colon \pi_1M\to GL(n,{\mathbb C})\) of
the fundamental group of a compact, aspherical manifold. Some
topological invariants like the volume and the Chern-Simons
invariant can be computed by looking at \((B\rho)_*\left[M\right]\in
H_*(GL(n,{\mathbb C}))\), that is, the image of the fundamental class
\(\left[M\right]\in H_*(M)\) in the homology of the general linear
group. We will discuss topological properties of such invariants, in
particular their invariance under mutation.
|
