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Nonabelian Poincaré duality after stabilizing


Author: Jeremy Miller
Journal: Trans. Amer. Math. Soc. 367 (2015), 1969-1991
MSC (2010): Primary 55P48
DOI: https://doi.org/10.1090/S0002-9947-2014-06186-2
Published electronically: September 30, 2014
MathSciNet review: 3286505
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Abstract: We generalize the nonabelian Poincaré duality theorems of Salvatore and Lurie to the case of not necessarily grouplike $ E_n$-algebras (in the category of spaces). We define a stabilization procedure based on McDuff's ``bringing points in from infinity'' maps. For open connected parallelizable $ n$-manifolds, we prove that, after stabilizing, the topological chiral homology of $ M$ with coefficients in an $ E_n$-algebra $ A$, $ \int _M A$, is homology equivalent to $ Map^c(M,B^n A)$, the space of compactly supported maps to the $ n$-fold classifying space of $ A$.


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Jeremy Miller
Affiliation: Department of Mathematics, CUNY Graduate Center, 365 Fifth Avenue, New York, New York 10016
Email: jmiller@gc.cuny.edu

DOI: https://doi.org/10.1090/S0002-9947-2014-06186-2
Received by editor(s): September 28, 2012
Received by editor(s) in revised form: March 20, 2013
Published electronically: September 30, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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