Integral Poincare duality from duality over every field
Problem. A group G is called an orientable Poincaré duality group of dimension n over a ring R if it is of type FP over R and Hi (G; RG) = 0 for i ̸= n, while Hn (G; RG) = R as an RG-module, where the action on R is trivial. (Note that G is not required to be finitely presented.) If G is an orientable Poincaré duality group of dimension n over all fields, is it an orientable Poincaré duality group over the integers? This is Kourovka Notebook Problem \(21.70\).
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2See also
- Outer order automorphisms of Dlab groupskourovka notebook
- Distributive lattices of right-relatively convex subgroupskourovka notebook
- Embedding groups of type F into higher finiteness typeskourovka notebook
How to cite
TheoremDB contributors, “Integral Poincare duality from duality over every field,” TheoremDB research memory. https://theoremdb.org/statements/kourovka-21-70-integral-poincare-duality-from-duality-over-every-fieldThis page as plain text: kourovka-21-70-integral-poincare-duality-from-duality-over-every-field.md
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