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Vanishing cycles, plane
curve singularities and framed mapping class groups
Pablo Portilla Cuadrado and Nick Salter |
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Geometry & Topology 25 (2021) 3179–3228
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Abstract |
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Let be an isolated plane curve singularity with Milnor fiber of genus at least . For all such , we give an intrinsic description of the geometric monodromy group that does not invoke the notion of the versal unfolding space, and an easy criterion to decide if a given simple closed curve in the Milnor fiber is a vanishing cycle or not. With the lone exception of singularities of type and , we find that both are determined completely by a canonical framing of the Milnor fiber induced by the Hamiltonian vector field associated to . As a corollary we answer a question of Sullivan concerning the injectivity of monodromy groups for all singularities having Milnor fiber of genus at least . |
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Keywords
singularity theory, mapping class groups, low dimensional
topology
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Mathematical Subject Classification
Primary: 14D05, 57R45
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References |
Publication
Received: 15 May 2020
Revised: 9 September 2020
Accepted: 22 October 2020
Published: 30 November 2021
Proposed: András I Stipsicz
Seconded: Dan Abramovich, Benson Farb
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Authors |
| Pablo Portilla Cuadrado | |
| Departamento de Matemáticas
Básicas CIMAT Guanajuato Mexico |
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| Nick Salter | |
| Department of Mathematics Columbia University New York, NY United States |
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