61 research outputs found
Godel and the Integrated Self, or: On the Philosopher's Second Sailing
This article considers Godel's remarks on Plato's dialogueEuthyphro, which he made in conversation with the proof theorist Sue Toledo in the years 1972-1975.Peer reviewe
Topological equivalence and rigidity of flows on certain solvmanifolds
Given a Lie group and a lattice in , a one-parameter subgroup of is said to be rigid if for any other one-parameter subgroup , the flows induced by and on (by right translations) are topologically orbit-equivalent only if they are affinely orbit-equivalent. It was previously known that if is a simply connected solvable Lie group such that all the eigenvalues of , , are real, then all one-parameter subgroups of are rigid for any lattice in . Here we consider a complementary case, in which the eigenvalues of , , form the unit circle of complex numbers. Let be the semidirect product , where and are finite-dimensional real vector spaces and where the action of on the normal subgroup is such that the center of is a lattice in . We prove that there is a generic class of abelian lattices in such that any semisimple one-parameter subgroup (namely such that is diagonalizable over the complex numbers for all ) is rigid for (see Theorem 1.4). We also show that, on the other hand, there are fairly high-dimensional spaces of abelian lattices for which some semisimple are not rigid (see Corollary 4.3); further, there are non-rigid semisimple for which the induced flow is ergodic
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