By David B. Massey
The Milnor quantity is a strong invariant of an remoted, advanced, affine hyper floor singularity. It offers information in regards to the neighborhood, ambient, topological-type of the hyper floor, and the fidelity of the Milnor quantity all through a relations means that Thom's $a_f$ holds and that the neighborhood, ambient, topological-type is continuous within the relations. a lot of the usefulness of the Milnor quantity is because of the truth that it may be successfully calculated in an algebraic manner.The Le cycles and numbers are a generalization of the Milnor quantity to the environment of advanced, affine hyper floor singularities, the place the singular set is authorized to be of arbitrary size. As with the Milnor quantity, the Le numbers offer information in regards to the neighborhood, ambient, topological-type of the hyper floor, and the fidelity of the Le numbers all through a family members means that Thom's $a_f$ situation holds and that the Milnor fibrations are consistent through the kinfolk. back, a lot of the usefulness of the Le numbers is because of the truth that they are often successfully calculated in an algebraic manner.In this paintings, we generalize the Le cycles and numbers to the case of hyper surfaces inside of arbitrary analytic areas. We outline the Le-Vogel cycles and numbers, and end up that the Le-Vogel numbers keep watch over Thom's $a_f$ situation. We additionally end up a dating among the Euler attribute of the Milnor fibre and the Le-Vogel numbers. in addition, we provide examples which convey that the Le-Vogel numbers are successfully calculable. on the way to outline the Le-Vogel cycles and numbers, we require, and comprise, loads of history fabric on Vogel cycles, analytic intersection thought, and the derived type. additionally, to function a version case for the Le-Vogel cycles, we remember our past paintings at the Le cycles of an affine hyper floor singularity.
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