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}
}
  • David AyalaJ. Francis
  • 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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24 Citations
Highly Influential Citations
4
Background Citations
7
Methods Citations
2

24 Citations

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Duality and vanishing theorems for topologically trivial families of smooth h-cobordisms

Using the work of Dwyer, Weiss, and Williams we associate an invariant to any topologically trivial family of smooth h-cobordisms. This invariant is called the smooth structure class, and is closely…

The cobordism hypothesis

Assuming a conjecture about factorization homology with adjoints, we prove the cobordism hypothesis, after Baez-Dolan, Costello, Hopkins-Lurie, and Lurie.

Poincaré/Koszul duality for general operads

We record a result concerning the Koszul dual of the arity filtration on an operad. This result is then used to give conditions under which, for a general operad, the Poincare/Koszul duality arrow of…

A proof of the Dold$-$Thom theorem via factorization homology

The Dold$-$Thom theorem states that for a sufficiently nice topological space, M, there is an isomorphism between the homotopy groups of the infinite symmetric product of M and the homology groups of…

Derived Koszul duality and TQ-homology completion of structured ring spectra

References

SHOWING 1-10 OF 49 REFERENCES

Poincaré/Koszul Duality

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…

Spaces of particles on manifolds and generalized poincaré dualities

In this paper, we use a ‘local to global’ scanning process based on a construction of Segal to unify and generalize interesting results throughout the literature relating multi-configuration spaces…

Topological hypercovers and 1-realizations

Abstract.We show that if U* is a hypercover of a topological space X then the natural map hocolim U* → X is a weak equivalence. This fact is used to construct topological realization functors for the…

Homotopy algebra and iterated integrals for double loop spaces

This paper provides some background to the theory of operads, used in the first author's papers on 2d topological field theory (hep-th/921204, CMP 159 (1994), 265-285; hep-th/9305013). It is intended…

The Dold–Thom theorem via factorization homology

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…

Homotopy Invariant Algebraic Structures on Topological Spaces

Motivation and historical survey.- Topological-algebraic theories.- The bar construction for theories.- Homotopy homomorphisms.- Structures on based spaces.- Iterated loop spaces and actions on…

Local structures on stratified spaces

A spectrum-level Hodge filtration on topological Hochschild homology

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…

Higher Topos Theory

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…

Calculus III: Taylor Series

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…