J. Baez and L. Langford, Higher-dimensional algebra IV: 2-Tangles, to appear in Adv. Math.. Home/Search Document Details and Download
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This paper is cited in the following contexts:
Categorification - Baez, Dolan (1998) Self-citation (Baez) (Correct)
....fact that n categories with duals are more general than n groupoids is the reason why topological quantum field theory can give more refined information than homotopy theory. Recently progress has been made on the case n = 2, k = 2, which has also illuminated the theory of 2 braids in 4 dimensions [6, 7, 25, 43]. In general, we expect that in the stable range nTang k is equivalent to the stable n category of framed cobordisms . Also, the universal property of nTang k should give a k tuply monoidal n functor T : nTang k Pi n( Omega k S k ) 29 generalizing the Thom Pontryagin construction. For ....
J. Baez and L. Langford, Higher-dimensional algebra IV: 2-Tangles, to appear in Adv. Math..
State-sum Invariants of Knotted Curves and Surfaces from.. - Carter, Jelsovsky, al. (1999) Self-citation (Langford) (Correct)
....cocycles (in quantum doubles of finite groups) are used to show representations of a Hopf category form a braided monoidal 2 category. Our definition was derived from an attempt to construct a 2 functor from the braided 2 category of knotted surfaces as summarized in [1] and presented in detail in [2], to another 2 category constructed from quandles. The non invertibility for certain classical knots had been presumed since the 1920 s but proved first by Trotter [41] and subsequently by Kawauchi [31] and Hartley [19] see also [30] Fox [16] presented a non invertible knotted sphere using ....
Baez, J.; Langford, L., Higher-dimensional algebra IV: 2-Tangles, to appear in Adv. Math, preprint available at http://xxx.lanl.gov/abs/math.QA/9811139 .
Quandle Cohomology and State-sum Invariants of Knotted.. - Carter, Jelsovsky, al. (1999) (3 citations) Self-citation (Langford) (Correct)
....used to give examples of representations of a Hopf category in a braided monoidal 2 category using quantum groups of finite groups. Our definition was derived from an attempt to construct a 2 functor from the braided 2 category of knotted surfaces as summarized in [1] and presented in detail in [2], to another 2 category constructed from quandles. We do not propose categorical explanations in the current paper. However, we encourage the reader to pursue connections between braided moniodal 2 categories and trunks as defined in [13] 1.1 Organization. Section 2 contains the basic ....
Baez, J.; Langford, L., Higher-dimensional algebra IV: 2-Tangles, to appear in Adv. Math, preprint available at http://xxx.lanl.gov/abs/math.QA/9811139
2-Tangles - Baez, Langford (1997) Self-citation (Baez Langford) (Correct)
....is thus that the 2 category of unframed unoriented 2 tangles in 4 dimensions is the free semistrict braided monoidal 2 category with duals on one unframed self dual object . The proof appears in Langford s dissertation [17] and will be published as part of the Higher Dimensional Algebra series [4]. To appreciate this result, one needs some feeling for the topology and algebra involved: that is, for higher dimensional tangles and higher dimensional category theory. Thus we begin with a brief sketch of both, concentrating on the situation at hand. We omit many details, which can be found in ....
J. Baez and L. Langford, Higher-dimensional algebra IV: 2-Tangles, to appear in Adv. Math..
Computations of Quandle Cocycle Invariants of Knotted .. - Carter, Jelsovsky.. (1999) (1 citation) (Correct)
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Baez, J.; Langford, L., Higher-dimensional algebra IV: 2-Tangles, to appear in Adv. Math, preprint available at http://xxx.lanl.gov/abs/math.QA/9811139 .
Structures and Diagrammatics of Four Dimensional.. - Carter, Kauffman, al. (1998) (3 citations) (Correct)
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Baez, J.; Langford, L., Higher-dimensional algebra IV: 2-Tangles, to appear in Adv. Math.
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