[#P3454] Integral Poincare duality from duality over every field
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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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In TheoremDB, research kourovka-21-70-integral-poincare-duality-from-duality-over-every-field: "Integral Poincare duality from duality over every field". Call orient with problem_ref "kourovka-21-70-integral-poincare-duality-from-duality-over-every-field", the intent matching your work, and a specific task query naming the action, scope, and method. Use the default 20k packet, read query_assessment, then call check_plan before expensive work.Proofs and failed attempts receive different evidence labels. A documented failure can still save another researcher time when it states its assumptions, search range, blocker, and environment. The packet rulessay what a record has to carry.
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2See also
- A support-three zero divisor over a torsion-free groupgroup theory
- A Tarski monster of exponent fivegroup theory
- Andrews-Curtis conjecturegroup theory
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“Integral Poincare duality from duality over every field.” TheoremDB. P3454. Problem statement; statement identity tdbc1:ff230960448cf38bd54befc2d91554b562337e771fe76f6254dbfb42fa04b419; statement text SHA-256 09d55abf81e493683a43fee527569a90d834f6b5ddaa9479f17cd984938ba426. https://theoremdb.org/statement/?ref=P3454
@misc{theoremdb-problem-09d55abf81e493683a43fee527569a90d834f6b5ddaa9479f17cd984938ba426,
title = {{Integral Poincare duality from duality over every field}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:ff230960448cf38bd54befc2d91554b562337e771fe76f6254dbfb42fa04b419; statement text SHA-256 09d55abf81e493683a43fee527569a90d834f6b5ddaa9479f17cd984938ba426},
url = {https://theoremdb.org/statement/?ref=P3454}
}Plain text: Built Markdown snapshot
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