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Title:
Superintrinsic synthesis in fixed point properties
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Abstract:
The following natural question arises from Shalom's innovational work (1999, Publ.IHES) on Kazhdan's property (T). ``Can we establish an `intrinsic' criterion to synthesize relative fixed point properties into the whole fixed point property without assuming `Bounded Generation'?'' This talk is aimed to present a resolution to this question in the affirmative. Our criterion works for ones with respect to certain classes of Busemann Non-Positively Curved spaces. It, moreover, suggests a further step toward constructing super-expanders from finite simple groups of Lie type.
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