# 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…

### FIBERWISE POINCARÉ–HOPF THEORY AND EXOTIC SMOOTH STRUCTURES ON FIBER BUNDLES

- Mathematics
- 2021

We prove the Rigidity Conjecture of Goette and Igusa, which states that, after rationalizing, there are no stable exotic smoothings of manifold bundles with closed even dimensional fibers. The key…

### 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…

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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…

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