MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $G$ be a discrete group and K a subgroup of G . denote by $(\hat{H_K})^i$ the bounded cohomology groups of $K$ , and by $(\hat{H_G})^i$ the bounded cohomology groups of G.

then $(\hat{H_K})^i$ is embedded in $(\hat{H_G})^i$ ??

share|cite|improve this question
Cohomology with what coefficients? – Yemon Choi Oct 18 '11 at 19:26
up vote 3 down vote accepted

In general, no. There is not even a natural map (in general) in the direction you want.

There is a natural map in the opposite direction, namely restriction, and this is sometimes an embedding, but not always. See chapter 8.6 in "Continuous bounded cohomology of locally compact groups", Lecture Notes in Mathematics 1758

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.