Analytic and Nash equivalence relations of Nash maps

作者：Shiota Masahiro^*

来源：Bulletin of the London Mathematical Society, 2010, 42: 1055-1064.

DOI：10.1112/blms/bdq064

Let M and N be Nash manifolds, and f and g be Nash maps from M to N. If M and N are compact and if f and g are analytically R-L equivalent, then they are Nash R-L equivalent. In the local case, C(infinity) R-L equivalence of two Nash map germs implies Nash R-L equivalence. This shows a difference of Nash map germs and analytic map germs. Indeed, there are two analytic map germs from (R(2), 0) to (R(4), 0) which are C(infinity) R-L equivalent but not analytically R-L equivalent.

• 出版日期2010-12