Abstract
A theorem of Lambrechts and Stanley is used to find the rational cohomology of the complement of an embedding S4n−1 → S2n ×Sm as a module and demonstrate that it is not necessarily determined by the map induced on cohomology by the embedding, nor is it a trivial extension. This demonstrates that the theorem is an improvement on the classical Lefschetz duality.
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References
Félix, Y., Halperin, S. and Thomas, J. C., Rational homotopy theory, Graduate Texts in Mathematics, 205, Springer-Verlag, New York, 2001.
Klein, J. R., Poincaré duality embeddings and fiberwise homotopy theory, Topology, 38(3), 1999, 597–620.
Klein, J. R., Poincaré duality spaces, Surveys on Surgery Theory, Vol. 1, Ann. of Math. Stud., Vol. 145, Princeton Univ. Press, Princeton, NJ, 2000, 135–165.
Lambrechts, P. and Stanley, D., Algebraic models of Poincaré embeddings, Algebr. Geom. Topol., 5, 2005, 135–182 (electronic).
Wall, C. T. C., Classification problems in differential topology. VI. Classification of (s -1)-connected (2s + 1)-manifolds, Topology, 6, 1967, 273–296.
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The work was supported by the National Science and Engineering Research Council of Canada.
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Lambrechts, P., Lane, J. & Stanley, D. An example using improved Lefschetz duality. Chin. Ann. Math. Ser. B 38, 1269–1274 (2017). https://doi.org/10.1007/s11401-017-1035-3
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DOI: https://doi.org/10.1007/s11401-017-1035-3