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Poincaré duality algebras mod two
<span title="">2010</span>
<i title="Elsevier BV">
<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/37jjomjmvfhrzf3di2gjnrrfuu" style="color: black;">Advances in Mathematics</a>
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We study Poincaré duality algebras over the field F F F 2 of two elements. After introducing a connected sum operation for such algebras we compute the corresponding Grothendieck group of surface algebras (i.e., Poincaré algebras of formal dimension 2). We show that the corresponding group for 3-folds (i.e., algebras of formal dimension 3) is not finitely generated, but does have a Krull-Schmidt property. We then examine the isomorphism classes of 3-folds with at most three generators of degree
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... 3, provide a complete classification, settle which such occur as the cohomology of a smooth 3-manifold, and list separating invariants. The closing section and Appendix A provide several different means of constructing connected sum indecomposable 3-folds.
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