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

@article{Amabel2019LecturesOF,
  title={Lectures on Factorization Homology, ∞-Categories, and Topological Field Theories},
  author={Araminta Amabel and Artem Kalmykov and Lukas Muller and Hiro Tanaka},
  journal={arXiv: Algebraic Topology},
  year={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 homotopy theorists. 
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On quantum obstruction spaces and higher codimension gauge theories

References

SHOWING 1-10 OF 78 REFERENCES

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…

On the Classification of Topological Field Theories

This paper provides an informal sketch of a proof of the Baez-Dolan cobordism hypothesis, which provides a classification for extended topological quantum field theories.

Free factorization algebras and homology of configuration spaces in algebraic geometry

We provide a construction of free factorization algebras in algebraic geometry and link factorization homology of a scheme with coefficients in a free factorization algebra to the homology of its…

ZERO-POINTED MANIFOLDS

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…

The cobordism hypothesis

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

Simplicial Homotopy Theory

Simplicial sets, model categories, and cosimplicial spaces: applications for homotopy coherence, results and constructions, and more.

Configuration spaces are not homotopy invariant

FACTORIZATION HOMOLOGY OF ENRICHED ∞-CATEGORIES

For an arbitrary symmetric monoidal∞-category V, we define the factorization homology of V-enriched∞-categories over (possibly stratified) 1-manifolds and study its basic properties. In the case that…

A-infinity algebras, modules and functor categories

In this survey, we first present basic facts on A-infinity algebras and modules including their use in describing triangulated categories. Then we describe the Quillen model approach to A-infinity…

A Survey of (∞, 1)-Categories

In this paper we give a summary of the comparisons between different definitions of so-called (∞, 1)-categories, which are considered to be models for ∞-categories whose n-morphisms are all…
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