Lantern Illumination

A lantern lemma

We show that in the mapping class group of a surface any relation between Dehn twists of the form T j xT k y = M (M a multitwist) is the lantern relation, and any relation of the form (TxTy) k = M (where Tx commutes with M ) is the 2-chain relation. AMS Classification 57M07; 20F38, 57N05

Applications of the Lantern Identity

The purpose of this note is to unify the role of the lantern identity in the proof of several finiteness theorems. In particular, we show that for every nonnegative integer m, the vector space (over the rationals) of type m (resp. T -type m) invariants of integral homology 3-spheres are finite dimensional. These results have already been obtained by [Oh] and [GL2] respectively; our derivation h...

A Magic Lantern Data Projector

The Magic Lantern Data Projector allows a performer-participant to build sculptural glass forms that are projected, then algorithmically processed. The device re-envisions magic lantern slides as transparent, multifaceted three-dimensional glass boxes. The projected image is a palimpsest of coloured transparent glass forms (Figure 1). Servomotors position the boxes in front of a camera lens, wh...

The solemn lady with the lantern.

SLM SLM illumination Reference illumination Holographic

A prototype reflective spatial light modulator (SLM) system has been developed for writing megabit pages of data into a holographic medium at a rate of 12 pages per minute. The SLM is based upon a crystalline-silicon reflective active-matrix array with integrated data drivers, using liquid crystal (LC) electrooptics and a personal computer system with an interface to provide data. The LC has be...