A festive introduction to cohomology with twisted coefficients

Nigel Ray (University of Manchester)

Frank Adams 2,

Cohomology with twisted coefficients arises naturally in several areas of algebraic topology, and plays a significant role in studying many interesting and important examples involving vector bundles. Usually, however, standard textbooks focus on cases "with trivial twisting", as a way of pacifying their readership. In this talk I aim to  return to Rene Thom's seminal work of the 1950s (on what are now called "Thom spaces"), and try to explain how it illuminates the path through the jungle of twisted coefficients of a certain specific type. I shall also attempt to include more recent work of Martin Cadek, from around 1999, which seems to offer a novel viewpoint that has received less attention than it may deserve. I hope it will be possible to present the material in celebratory style, given the proximity of the winter solstice:-)

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