Real map germs and higher open books

Abstract

We present a general criterion for the existence of open book structures defined by real map germs $(\bR^m, 0) \to (\bR^p, 0)$, where $m>p\ge 2$, with isolated critical point. We show that this is satisfied by weighted-homogeneous maps. We also derive sufficient conditions in case of map germs with isolated critical value.

12 pages

References in corpus (9)

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• Lectures on open book decompositions and contact structures
• Real map germs and higher open books
• The Zariski-Lefschetz principle for higher homotopy groups of nongeneric pencils
• Singularities and Topology of Meromorphic Functions
• Real Analytic Milnor Fibrations and a Strong Łojasiewicz Inequality
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• Non-degenerate mixed functions
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Cited by in corpus (16)

• Real map germs and higher open books
• Fibrations of highly singular map germs
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• Images of analytic map germs, and singular fibrations
• Equivalence of real Milnor's fibrations for quasi homogeneous singularities
• New examples of Neuwirth-Stallings pairs and non-trivial real Milnor fibrations
• Milnor-Hamm sphere fibrations and the equivalence problem
• Equivalence of Milnor and Milnor-Lê fibrations for real analytic maps
• On singular maps with local fibration
• Characterizations of trivial maps in 3-dimensional real Milnor fibers
• Refinements of Milnor's Fibration Theorem for Complex Singularities
• On the Milnor fibration for $f(z)\bar{g}(z)$ II
• Inner and Partial non-degeneracy of mixed functions
• Some remarks about $\rho$-regularity for real analytic maps
• Tame deformations of highly singular function germs
• Global index of real polynomials