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27 votes
2 answers
796 views

Is there a flat manifold with trivial first homology?

Is there a closed flat manifold whose fundamental group has trivial abelianization? The famous Hantzsche–Wendt flat manifold has fundamental group with finite abelianization.
7 votes
1 answer
463 views

Cohomology of the mapping class group of a non-orientable surface?

What is the low degree cohomology of the mapping class group of a non-orientable surface? More specifically, what is the universal central extension of the mapping class group of a non-orientable ...