On the Classification of Topological Field Theories

@article{Lurie2008OnTC,
  title={On the Classification of Topological Field Theories},
  author={Jacob Lurie},
  journal={arXiv: Category Theory},
  year={2008}
}
  • J. Lurie
  • Published 2008
  • Mathematics
  • arXiv: Category Theory
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. 
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References

SHOWING 1-10 OF 27 REFERENCES
Derived Algebraic Geometry III: Commutative Algebra
This paper describes a higher-categorical version of the theory of colored operads, giving applications to the study of commutative ring spectra.
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 theExpand
Lectures on tensor categories and modular functors
Introduction Braided tensor categories Ribbon categories Modular tensor categories 3-dimensional topological quantum field theory Modular functor Moduli spaces and complex modular functorExpand
The homotopy type of the cobordism category
The embedded cobordism category under study in this paper generalizes the category of conformal surfaces, introduced by G. Segal in [S2] in order to formalize the concept of field theories. Our mainExpand
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 allExpand
Vers une axiomatisation de la théorie des catégories supérieures.
We define a notion of "theory of (1,infty)-categories", and we prove that such a theory is unique up to equivalence.
Topological conformal field theories and Calabi–Yau categories
Abstract This is the first of two papers which construct a purely algebraic counterpart to the theory of Gromov–Witten invariants (at all genera). These Gromov–Witten type invariants depend on aExpand
(Infinity,2)-Categories and the Goodwillie Calculus I
The bulk of this paper is devoted to the comparison of several models for the theory of (infinity,2)-categories: that is, higher categories in which all k-morphisms are invertible for k > 2 (the caseExpand
Stable homology of automorphism groups of free groups
Homology of the group Aut(F_n) of automorphisms of a free group on n generators is known to be independent of n in a certain stable range. Using tools from homotopy theory, we prove that in thisExpand
The geometry of iterated loop spaces
Operads and -spaces.- Operads and monads.- A? and E? operads.- The little cubes operads .- Iterated loop spaces and the .- The approximation theorem.- Cofibrations and quasi-fibrations.- The smashExpand
...
1
2
3
...