Positive factorizations of pseudoperiodic homeomorphisms. (English) Zbl 1465.37057
Summary: We generalize a classical result concerning smooth germs of surfaces, by proving that monodromies on links of isolated complex surface singularities associated with reduced holomorphic map germs admit a positive factorization. As a consequence of this and a topological characterization of these monodromies by A. Pichon [Ann. Inst. Fourier 51, No. 2, 337–374 (2001; Zbl 0971.32013)], we conclude that a pseudoperiodic homeomorphism on an oriented surface with boundary with positive fractional Dehn twist coefficients and screw numbers, admits a positive factorization. We use the main theorem to give a sufficiency criterion for certain pseudoperiodic homeomorphisms with negative screw numbers to admit a positive factorization.
MSC:
| 37E30 | Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces |
| 37C55 | Periodic and quasi-periodic flows and diffeomorphisms |
| 32S25 | Complex surface and hypersurface singularities |
| 14B07 | Deformations of singularities |
| 32S30 | Deformations of complex singularities; vanishing cycles |
| 32S50 | Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants |
Citations:
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