This is an announcement for the paper "Decompositions, approximate structure, transference, and the Hahn-Banach theorem" by W. T. Gowers.
Abstract: This paper is partly a survey of certain kinds of results and proofs in additive combinatorics, and partly a discussion of how useful the finite-dimensional Hahn-Banach theorem can be. The most interesting single result is probably a simpler proof of a key step in the proof of the Green-Tao theorem, but several other applications of the method are given. A similarly simplified proof of the Green-Tao transference principle was obtained independently (and expressed in a rather different language) by Reingold, Trevisan, Tulsiani and Vadhan.
Archive classification: math.CO math.FA
Mathematics Subject Classification: 05D99
Remarks: 48 pages
The source file(s), newtransfer6.tex: 157325 bytes, is(are) stored in gzipped form as 0811.3103.gz with size 46kb. The corresponding postcript file has gzipped size 191kb.
Submitted from: wtg10@dpmms.cam.ac.uk
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