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A very short proof of Forester's rigidity result

https://www.youtube.com/watch?v=kJpZh0Onysc

Mark Fell and Roc Jiménez de Cisneros

Generative piece for Matthew Ritchie's The Morning Line anti-pavillion at the 3rd Biennial of Contemporary Art of Seville. 2008.

The deformation space of a simplicial G-tree T is the set of G-trees which can be obtained from T by some collapse and expansion moves, or equivalently, which have the same elliptic subgroups as T. We give a short proof of a rigidity result by Forester which gives a sufficient condition for a deformation space to contain an Aut(G)-invariant G-tree. This gives a sufficient condition for a JSJ splitting to be invariant under automorphisms of G. More precisely, the theorem claims that a deformation space contains at most one strongly slide-free G-tree, where strongly slide-free means the following: whenever two edges e_1, e_2 incident on a same vertex v are such that G_{e_1} is a subset of G_{e_2}, then e_1 and e_2 are in the same orbit under G_v.

Seville 2008

Istanbul 2010

When asked, "why doesn’t your sound move from speaker to speaker?" prominent sound artist Yasunao Tone replied, "why is this necessary when the audience can move around the sound?" A very short proof of Forester's rigidity result develops this position: rather than moving around the audience, as is typical of multispeaker pieces, here the sound itself is rigid. The listener is placed within and moves through a complex matrix of digital oscillators, each producing one component of the overall sound: a series of precisely synchronized and desynchronized pulses, each one static in a spatial dimension but evolving in a harmonic one. This reversal of roles undermines the traditional placement of a static listener and frontal stage that originated in Italian Renaissance palaces, a paradigm comparable to the invention of one-point perspective in the visual arts. This "first-person" model of musical performance is still evident today in nearly all electro-acoustic and computer music—complete with all the baggage of its visual counterpart. (MF / RJC)

links

tba21 http://www.tba21.org/pavilions/49/page_2?category=pavilions
seville biennial http://www.fundacionbiacs.com/biacs3/
where we got the name from http://www.msp.warwick.ac.uk/gt/2003/07/p010.xhtml


© mark fell, modified March 14, 2013, at 05:47 AM edit print