dynamics of infinite dimensional groups and ramsey tpye phenomena

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1、rtp-impa"ii2005/5/12page1iiDynamicsofinnite-dimensionalgroupsandRamsey-typephenomenaVladimirPestovMay12,2005iiiirtp-impa"ii2005/5/12page2iiiiiirtp-impa"ii2005/5/12pageiiiContentsPrefaceiii0Introduction11TheRamsey{Dvoretzky{Milmanphenomenon171.1Finiteosci

2、llationstability................171.2Firstexample:thesphereS1..............271.2.1FiniteoscillationstabilityofS1........271.2.2Concentrationofmeasureonspheres......321.3Secondexample:niteRamseytheorem........411.4Counter-example:orderedpairs.............472

3、Thexedpointoncompactaproperty492.1Extremelyamenablegroups...............492.2Threemainexamples...................552.2.1Example:theunitarygroup...........552.2.2Example:thegroupAut(Q;).........602.2.3Counter-example:theinnitesymmetricgroup622.3Equivariant

4、compactication..............632.4Essentialsetsandtheconcentrationproperty.....662.5Veechtheorem......................712.6Bigsets..........................762.7Invariantmeans......................813Levygroups953.1Unitarygroupwiththestrongtopology........9

5、5iiiiirtp-impa"ii2005/5/12pageiiiiiiCONTENTS3.2Groupofmeasurablemaps...............983.2.1Constructionandexample............983.2.2Martingales....................1013.2.3Unitarygroupsofoperatoralgebras......1103.3Groupsoftransformationsofmeasurespaces.....1

6、153.3.1Maurey'stheorem................1153.3.2Groupofmeasure-preservingtransformations.1173.3.3Fullgroups....................1233.4GroupofisometriesoftheUrysohnspace.......1333.4.1Urysohnuniversalmetricspace.........1333.4.2Isometrygroup..................143

7、3.4.3Approximationbynitegroups.........1463.5Levygroupsandspatialactions.............1554Minimal ows1654.1Universalminimal ow..................1654.2Groupofcirclehomeomorphisms............1684.2.1Example......................1684.2.2Largeextremelyamenables

8、ubgroups......1694.3Innitesymmetricgroup.................1734.4MaximalchainsandUspenskij'stheorem........1764.5AutomorphismgroupsofFra•ssestructures......1804.5.1Fra•ssetheory..............