# 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} }

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.

## 24 Citations

### Poincaré/Koszul Duality

- MathematicsCommunications in Mathematical Physics
- 2019

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…

### The Dold–Thom theorem via factorization homology

- MathematicsJournal of Homotopy and Related Structures
- 2018

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…

### Lectures on Factorization Homology, ∞-Categories, and Topological Field Theories

- Mathematics
- 2019

These are notes from an informal mini-course on factorization homology, infinity-categories, and topological field theories. The target audience was imagined to be graduate students who are not…

### Spectral Algebra Models of Unstable $$v_n$$-Periodic Homotopy Theory

- MathematicsBousfield Classes and Ohkawa's Theorem
- 2020

We give a survey of a generalization of Quillen-Sullivan rational homotopy theory which gives spectral algebra models of unstable v_n-periodic homotopy types. In addition to describing and…

### Traces for factorization homology in dimension 1

- Mathematics
- 2021

We construct a circle-invariant trace from the factorization homology of the circle trace : ∫ α S1 End(V ) −→ 1 associated to a dualizable object V ∈ X in a symmetric monoidal ∞-category. This proves…

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

- Mathematics
- 2021

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

- Mathematics
- 2017

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

- MathematicsHomology, Homotopy and Applications
- 2022

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

- Mathematics
- 2017

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

- MathematicsAdvances in Mathematics
- 2019

## References

SHOWING 1-10 OF 49 REFERENCES

### Poincaré/Koszul Duality

- MathematicsCommunications in Mathematical Physics
- 2019

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

- Mathematics
- 2001

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

- Mathematics
- 2004

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

- Mathematics
- 1994

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

- MathematicsJournal of Homotopy and Related Structures
- 2018

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

- Mathematics
- 1973

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

### A spectrum-level Hodge filtration on topological Hochschild homology

- Mathematics
- 2014

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

- Philosophy, Mathematics
- 2009

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

- Mathematics
- 2003

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…