ANOSOV THEOREM FOR COINCIDENCES ON SPECIAL SOLVMANIFOLDS OF TYPE (R)

作者：Ha Ku Yong^*; Lee Jong Bum; Penninckx Pieter

来源：Proceedings of the American Mathematical Society, 2011, 139(6): 2239-2248.

DOI：10.1090/S0002-9939-2010-10721-9

• Nielsen coincidence number
• solvmanifold

Suppose that S and S' are simply connected solvable Lie groups of type (R) with the same dimension. We show that the Lefschetz coincidence numbers of maps f,g : Gamma\S -> Gamma'\S' between special solvmanifolds Gamma\S -> Gamma'\S' can be computed algebraically as follows:
L(f,g) = det(G(*) - F(*)),
where F(*), G(*) are the matrices, with respect to any preferred bases, of morphisms of Lie algebras induced by f and g. This generalizes a recent result by S. W. Kim and J. B. Lee to special solvmanifolds of type (R). Moreover, we can drop the dimension match condition imposed in the latter result.

• 出版日期2011-6