分野別セミナー

【講演要旨】Let π be a discrete group, and let G be a compact connected Lie group. There is a natural map,
Hom(π, G)_0 → map_∗(Bπ, BG)_0, from the null component of the space of homomorphisms to that of the space of
based maps. When π is a surface group, Atiyah and Bott studied this map and showed surjectivity in rational
cohomology. In this talk, we will consider this map when π = Z^m for m ≥ 3. Under this condition, we will give a
necessary and sufficient condition for this map to be surjective in rational cohomology.