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Published online by Cambridge University Press:  02 July 2019

David Ayala
Department of Mathematics, Montana State University, Bozeman, MT 59717, USA (
John Francis
Department of Mathematics, Northwestern University, Evanston, IL 60208-2370, USA (


We formulate a theory of pointed manifolds, accommodating both embeddings and Pontryagin–Thom collapse maps, so as to present a common generalization of Poincaré duality in topology and Koszul duality in ${\mathcal{E}}_{n}$ -algebra.

Research Article
© Cambridge University Press 2019

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DA was partially supported by ERC adv.grant no.228082, and by the National Science Foundation under Award 0902639 and Award 1507704. JF was supported by the National Science Foundation under Award 1207758 and Award 1508040.


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