# ZERO-POINTED MANIFOLDS

@article{Ayala2014ZEROPOINTEDM,
title={ZERO-POINTED MANIFOLDS},
author={David Ayala and John Francis},
journal={Journal of the Institute of Mathematics of Jussieu},
year={2014},
volume={20},
pages={785 - 858}
}
• Published 9 September 2014
• Mathematics
• Journal of the Institute of Mathematics of Jussieu
Abstract 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.
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We prove a duality for factorization homology which generalizes both usual Poincaré duality for manifolds and Koszul duality for $${\mathcal{E}_n}$$En-algebras. The duality has application to the
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We give a new proof of the classical Dold–Thom theorem using factorization homology. Our method is direct and conceptual, avoiding the Eilenberg–Steenrod axioms entirely in favor of a more general
• Mathematics
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Motivation and historical survey.- Topological-algebraic theories.- The bar construction for theories.- Homotopy homomorphisms.- Structures on based spaces.- Iterated loop spaces and actions on
We define a functorial spectrum-level filtration on the topological Hochschild homology of any commutative ring spectrum R, and more generally the factorization homology $$R \otimes X$$R⊗X for any
This purpose of this book is twofold: to provide a general introduction to higher category theory (using the formalism of "quasicategories" or "weak Kan complexes"), and to apply this theory to the
We study functors from spaces to spaces or spectra that preserve weak homotopy equivalences. For each such functor we construct a universal n-excisive approximation, which may be thought of as its