SCOTT J. MORRISON

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Skein theory for the D 2n planar algebras. Abstract We give a combinatorial description of the " D 2n planar algebra " , by giving generators and relations. This includes a direct proof that the relations are consistent, as well as a complete description of the associated tensor category and its principal graph. While we use the usual langauge of subfactor(More)
We reconsider the su 3 link homology theory defined by Khovanov in [9] and generalized by Mackaay and Vaz in [15]. With some slight modifications , we describe the theory as a map from the planar algebra of tangles to a planar algebra of (complexes of) 'cobordisms with seams' (actually, a 'canopo-lis'), making it local in the sense of Bar-Natan's local su 2(More)
The border region of Baja California in Mexico and California in the United States is a biologically diverse and unique landscape that forms a portion of one of the world's global biodiversity hotspots. While the natural resources of this border region are continuous and interconnected, land conservation practices on either side of the international(More)
The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. ABSTRACT Growing interest in 21 cm tomography has led to the design and construction of broad-band radio interferometers with low noise, moderate angular resolution, high spectral resolution, and wide fields of view. With characteristics(More)
We give a simple proof of Lee's result from [5], that the dimension of the Lee variant of the Khovanov homology of a c –component link is 2 c , regardless of the number of crossings. Our method of proof is entirely local and hence we can state a Lee-type theorem for tangles as well as for knots and links. Our main tool is the " Karoubi envelope of the(More)
The Transition Region and Coronal Explorer (TRACE) satellite , launched 2 April 1998, is a NASA Small Explorer (SMEX) that images the solar photosphere, transition region and corona with unprecedented spatial resolution and temporal continuity. To provide continuous coverage of solar phenomena, TRACE is located in a sun-synchronous polar orbit. The 700(More)
While topologists have had possession of possible counterexamples to the smooth 4-dimensional Poincaré conjecture (SPC4) for over 30 years, until recently no invariant has existed which could potentially distinguish these examples from the standard 4-sphere. Rasmussen's s-invariant, a slice obstruction within the general framework of Khovanov homology,(More)
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We construct link invariants using the D 2n subfactor planar algebras, and use these to prove new identities relating certain specializations of colored Jones polynomials to specializations of other quantum knot polynomials. These identities can also be explained by coincidences between small modular categories involving the even parts of the D 2n planar(More)