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The purpose of this note is to announce a new isotopy invariant of oriented links of tamely embedded circles in 3-space. We represent links by plane projections, using the customary conventions that the image of the link is a union of transversely intersecting immersed curves, each provided with an orientation, and undercrossings are indicated by broken… (More)

- Louis Crane, David Yetter
- 1993

1. Introduction In recent years, it has been discovered that invariants of three dimensional topological objects, such as links and three dimensional manifolds, can be constructed from various tools of mathematical physics, such as Von Neumann algebras [1], Quantum Groups [2], and Rational Conformal Field Theories [3]. Since these different structures lead… (More)

- David N. Yetter
- J. Symb. Log.
- 1990

We provide, with proofs, a complete description of the authors' construction of state-sum invariants announced in [CY], and its generalization to an arbitrary (artinian) semisimple tortile category. We also discuss the relationship of these invariants to generalizations of Broda's surgery invariants [Br1,Br2] using techniques developed in the case of the… (More)

- Louis Crane, David N. Yetter
- Applied Categorical Structures
- 2005

Using the theory of measurable categories developped in [Yet03], we provide a notion of representations of 2-groups more well-suited to physically and geometrically interesting examples than that using 2-VECT (cf. [KV94]). Using this theory we sketch a 2-categorical approach to the state-sum model for Lorentzian quantum gravity proposed in [CY03], and… (More)

- David N. Yetter
- 1999

The 2-category of all small categories equivalent to a (finite) cartesian product of the category of finite dimensional vector spaces over a fixed field, left-exact functors, and natural transformations has structures closely mimicking those found in ordinary linear algebra. We examine these structures, the relation of this category to the 2-categories and… (More)

- GEOFF EHRMAN, ATA GURPINAR, MATTHEW THIBAULT, DAVID YETTER
- 2005

This paper summarizes substantive new results derived by a student team (the first three authors) under the direction of the fourth author at the 2005 session of the KSU REU " Brainstorming and Barnstorming ". The main results are a decomposition theorem for quandles in terms of an operation of 'semidisjoint union' showing that all finite quandles… (More)

- David N. Yetter
- J. Comb. Theory, Ser. B
- 1990