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- W2964328632 abstract "We use topological methods to prove a semicontinuity property of the Hodge spectra for analytic germs defined on an isolated surface singularity. For this we introduce an analogue of the Seifert matrix (the fractured Seifert matrix), and of the Levine–Tristram signatures associated with it, defined for null-homologous links in arbitrary three dimensional manifolds. Moreover, we establish Murasugi type inequalities in the presence of cobordisms of links. It turns out that the fractured Seifert matrix determines the Hodge spectrum and the Murasugi type inequalities can be read as spectrum semicontinuity inequalities. On utilise des méthodes topologiques afin de démontrer la semi-continuité des spectres de Hodge pour les germes de fonctions analytiques définies sur une surface ayant une singularité isolée. Pour cela on introduit un analogue de la matrice de Seifert (appelée matrice brisée de Seifert) et des signatures de Levine–Tristam associées à la matrice brisée. Ces analogues sont construits pour chaque entrelac homologiquement trivial dans une variété réelle de dimension trois. De plus on démontre des inégalités à la Murasugi pour un cobordisme des entrelacs homologiquement triviaux. Il s'avère que la matrice brisée de Seifert détermine le spectre de Hodge. De plus les inégalités à la Murasugi peuvent être interprétées comme semi-continuité de spectre de Hodge." @default.
- W2964328632 created "2019-07-30" @default.
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- W2964328632 date "2015-05-01" @default.
- W2964328632 modified "2023-10-17" @default.
- W2964328632 title "The Hodge spectrum of analytic germs on isolated surface singularities" @default.
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- W2964328632 doi "https://doi.org/10.1016/j.matpur.2014.10.007" @default.
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