Groups, Geometry, and Dynamics


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Volume 9, Issue 3, 2015, pp. 917–974
DOI: 10.4171/GGD/332

Published online: 2015-10-29

Homological and Bloch invariants for $\mathbb Q$-rank one spaces and flag structures

Inkang Kim[1], Sungwoon Kim[2] and Thilo Kuessner[3]

(1) KIAS, Seoul, South Korea
(2) Jeju National University, South Korea
(3) KIAS, Seoul, South Korea

We use group homology to define invariants in algebraic K-theory and in an analogue of the Bloch group for $\mathbb Q$-rank one lattices and for some other geometric structures. We also show that the Bloch invariants of CR structures and of ag structures can be recovered by a fundamental class construction.

Keywords: Group (co)holomology, Bloch group, semisimple Lie group

Kim Inkang, Kim Sungwoon, Kuessner Thilo: Homological and Bloch invariants for $\mathbb Q$-rank one spaces and flag structures. Groups Geom. Dyn. 9 (2015), 917-974. doi: 10.4171/GGD/332