A generalized Join theorem for real analytic singularities
In this paper, we show a generalized Join theorem for real analytic singularities. For complex singularities, this theorem was proved by A. Némethi.
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arXiv subjects
Kazumasa Inaba
Publications and source records attributed to Kazumasa Inaba.
Join theorem for real analytic singularities
Let f_1 and f_2 be real analytic germs of independent variables. In this paper, we assume that f_1, f_2 and f = f_1 + f_2 satisfy a_f -condition. Then we show that the tubular Milnor fiber of f is homotopy equivalent to the join of tubular Milnor fibers of f_1 and f_2.
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On the number of cusps of deformations of complex polynomials
Let f be a 1-variable complex polynomial such that f has a singularity at the origin. In the present paper, we show that there exists a deformation of f which has only fold singularities and cusps as singularities of a real polynomial map from the plane to the plane. We then calculate the number of cusps of a deformation in a sufficiently small neighborhood of the origin.
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Topology of the Milnor fibrations of polar weighted homogeneous polynomials
In the present paper, we study deformations of polar weighted homogeneous polynomials which are also polar weighted homogeneous polynomials. We describe a round handle decomposition of the Milnor fibration of a deformation of a polar weighted homogeneous polynomial concretely and give the number of round handles by the number of positive and negative components of the links of singularities appearing before and after the deformation. We also give a formula of characteristic polynomials of these singularities by using the decomposition of the monodromy of the Milnor fibration induced by a round handle decomposition.
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Topology of mixed hypersurfaces of cyclic type
We study a simplicial mixed polynomial of cyclic type and its associated weighted homogeneous polynomial. In the present paper, we show that their links are diffeomorphic and their Milnor fibrations are isomorphic.
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On linear deformations of Brieskorn singularities of two variables into generic maps
In this paper, we study deformations of Brieskorn polynomials of two variables obtained by adding linear terms consisting of the conjugates of complex variables and prove that the deformed polynomial maps have only indefinite fold and cusp singularities in general. We then estimate the number of cusps appearing in such a deformation. As a corollary, we show that a deformation of a complex Morse singularity with real linear terms has only indefinite folds and cusps in general and the number of cusps is 3.
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On deformations of isolated singularities of polar weighted homogeneous mixed polynomials
In the present paper, we deform isolated singularities of a certain class of polar weighted homogeneous mixed polynomials, and show that there exists a deformation which has only definite fold singularities and mixed Morse singularities.
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