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JOIN THEOREM FOR REAL ANALYTIC SINGULARITIES

Inaba, Kazumasa 大阪大学 DOI:10.18910/87485

2022.04

概要

Let f1 : (Rn, 0n) → (Rp, 0p) and f2 : (Rm, 0m) → (Rp, 0p) be analytic germs of independent variables, where n,m ≥ p ≥ 2. In this paper, we assume that f1, f2 and f = f1 + f2 satisfy af - condition. Then we show that the tubular Milnor fiber of f is homotopy equivalent to the join of tubular Milnor fibers of f1 and f2. If p = 2, the monodromy of the tubular Milnor fibration of f is equal to the join of the monodromies of the tubular Milnor fibrations of f1 and f2 up to homotopy.

参考文献

[1] R.N. Araujo dos Santos, Y. Chen and M. Tib ´ ar, ˘ Singular open book structures from real mappings, Cent. Eur. J. Math. 11 (2013), 817–828.

[2] E. Brieskorn: Beispiele zur Differentialtopologie von Singularit ¨aten, Invent. Math. 2 (1966), 1–14.

[3] D. Burghelea and A. Verona: Local homological properties of analytic sets, Manuscripta Math. 7 (1972), 55–66.

[4] J.L. Cisneros-Molina: Join theorem for polar weighted homogeneous singularities; in Singularities II, Contemp. Math. 475, Amer. Math. Soc., Providence, RI, 2008, 43–59.

[5] A. Dold: Partitions of unity in the theory of fibrations, Ann. of Math. 78 (1963), 223–255.

[6] A. Durfee: Fibered knots and algebraic singularities, Topology 13 (1974), 47–59.

[7] D. Eisenbud and W. Neumann: Three-Dimensional Link Theory and Invariants of Plane Curve Singularities, Annals of Mathematics Studies 110, Princeton University Press, Princeton, N.J., 1985.

[8] C. Eyral and M. Oka: Whitney regularity and Thom condition for families of non-isolated mixed singularities, J. Math. Soc. Japan. 70 (2018), 1305–1336.

[9] C. Gibson, K. Wirthmuller, A. du Plessis and E. Looijenga: Topological Stability of Smooth Mappings, ¨ Lecture Notes in Mathematics 552, Springer-Verlag, Berlin-New York, 1976.

[10] H. Hironaka: Subanalytic sets; in Number theory, Algebraic Geometry and Commutative Algebra, in Honor of Yasuo Akizuki, Kinokuniya, Tokyo, 1973, 453–493.

[11] K. Inaba: On the enhancement to the Milnor number of a class of mixed polynomials, J. Math. Soc. Japan, 66 (2014), 25–36.

[12] K. Inaba: On fibered links of singularities of polar weighted homogeneous mixed polynomials; in Singularities in Geometry and Topology 2011, Advanced Studies in Pure Mathematics 66 (2015), 81–92.

[13] M. Ishikawa: Plumbing constructions of connected divides and the Milnor fibers of plane curve singularities, Indag. Mathem., N.S., 13 (2002), 499–514.

[14] L.H. Kauffman and W.D. Neumann: Products of knots, branched fibrations and sums of singularities, Topology 16 (1977), 369–393.

[15] D. Lines: On odd-dimensional fibred knots obtained by plumbing and twisting, J. London. Math. Soc. 32 (1985), 557–571.

[16] D. Lines: Stable plumbing for high odd-dimensional fibred knots, Canad. Math. Bull. 30 (1987), 429–435.

[17] S. Lojasiewicz: Triangulation of semi-analytic set, Ann. Scuola Norm. Sup. Pisa Cl, Sci. 18 (1964), 449– 474.

[18] J. Milnor: Construction of universal bundles, II, Ann. of Math. 63 (1956), 430–436.

[19] J. Milnor: Singular points of complex hypersurfaces, Annals of Mathematics Studies 61, Princeton University Press, Princeton, N.J., 1968.

[20] W. Neumann and L. Rudolph: Unfoldings in knot theory, Math. Ann. 278 (1987), 409–439.

[21] W. Neumann and L. Rudolph: The enhanced Milnor number in high dimensions; in Differential Topology Proceedings, Siegen 1987, Lecture Notes in Math. 1350, Springer-Verlag, 1988, 109–121.

[22] W. Neumann and L. Rudolph: Difference index of vectorfields and the enhanced Milnor number, Topology, 29 (1990), 83–100.

[23] M. Oka: On the homotopy types of hypersurfaces defined by weighted homogeneous polynomials, Topology 12 (1973), 19–32.

[24] M. Oka: Non-degenerate complete intersection singularity, Hermann, Paris, 1997.

[25] M. Oka: Non-degenerate mixed functions, Kodai Math. J. 33 (2010), 1–62.

[26] M. Oka: On Milnor fibrations, af-condition and boundary stability, Kodai Math. J. 38 (2015), 581–603.

[27] M. Oka: On the Milnor fibration for f(z) ¯g(z), Eur. J. Math. 6 (2020), 998–1019.

[28] C.P. Rourke and B.J. Sanderson: Introduction to piecewise-linear topology, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 69, Springer-Verlag, New York-Heidelberg, 1972.

[29] K. Sakamoto: The Seifert matrices of Milnor fiberings defined by holomorphic functions, J. Math. Soc. Japan. 26 (1974), 714–721.

[30] K. Sakamoto: Milnor fiberings and their characteristic maps; in Manifolds-Tokyo 1973 (Proc. Internat. Conf., Tokyo, 1973), Univ. Tokyo Press, 1975, 145–150.

[31] M. Sebastiani and R. Thom: Un r´esultat sur la monodromie, Invent. Math. 13 (1971), 90–96.

[32] E.H. Spanier: Algebraic Topology, McGraw-Hill Book Company, New York, 1966.

[33] J. A. Wolf: Differentiable fibre spaces and mappings compatible with Riemannian metrics, Michigan Math. J. 11 (1964), 65–70.

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