Poincaré duality algebras mod two |
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Authors: | Larry Smith R.E. Stong |
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Affiliation: | a AG-Invariantentheorie, Mittelweg 3, D 37133 Friedland, Federal Republic of Germany b Department of Mathematics, University of Virginia, Charlottesville, VA 22904-4137, USA |
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Abstract: | We study Poincaré duality algebras over the field F2 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 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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Keywords: | 13A02 13A50 13-99 13P10 55S10 |
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