Higher-Dimensional Algebra and Topological Quantum Field Theory

Higher-Dimensional Algebra and Topological Quantum Field Theory (1995)

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by John C. Baez , James Dolan

Venue:	Jour. Math. Phys
Citations:	116 - 13 self

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Datum	Value	Source
TITLE	Higher-Dimensional Algebra and Topological Quantum Field Theory	user correction - Legacy Corrections
AUTHOR NAME	John C. Baez	SVM HeaderParse 0.1
AUTHOR AFFIL	Department of Mathematics; University of California	SVM HeaderParse 0.2
AUTHOR ADDR	Riverside CA 92521	SVM HeaderParse 0.1
AUTHOR NAME	James Dolan	SVM HeaderParse 0.1
AUTHOR AFFIL	Department of Mathematics; University of California	SVM HeaderParse 0.2
AUTHOR ADDR	Riverside CA 92521	SVM HeaderParse 0.1
ABSTRACT	The study of topological quantum field theories increasingly relies upon concepts from higher-dimensional algebra such as n-categories and n-vector spaces. We review progress towards a definition of n-category suited for this purpose, and outline a program in which n-dimensional TQFTs are to be described as n-category representations. First we describe a `suspension' operation on n- categories, and hypothesize that the k-fold suspension of a weak n-category stabilizes for k n + 2. We give evidence for this hypothesis and describe its relation to stable homotopy theory. We then propose a description of n- dimensional unitary extended TQFTs as weak n-functors from the `free stable weak n-category with duals on one object' to the n-category of `n-Hilbert spaces'. We conclude by describing n-categorical generalizations of deformation quantization and the quantum double construction. Introduction One important lesson we have learned from topological quantum field theory is that describ...	user correction - Legacy Corrections
YEAR	1995	INFERENCE
VENUE	Jour. Math. Phys	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
PAGES	6073--6105	INFERENCE
VOLUME	36	INFERENCE
CITATIONS	37 found	ParsCit 1.0