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- W4285429140 abstract "We give a simple way to study the isotypes of the homology of simplicial complexes with actions of finite groups, and use it for Milnor fibers of textsc{icis}. We study the homology of images of mappings $f_t$ that arise as deformations of complex map germs $f:(mathbb{C}^n,S)to(mathbb{C}^p,0)$, with $n<p$, and the behaviour of singularities (instabilities) in this context. We study two generalizations of the notion of image Milnor number $mu_I$ given by Mond and give a workable way of compute them, with Milnor numbers of textsc{icis}. We also study two unexpected traits when $p>n+1$: stable perturbations with contractible image and homology of $text{im} f_t$ in unexpected dimensions. We show that Houston's conjecture, $mu_I$ constant in a family implies excellency in Gaffney's sense, is false, but we give a proof for the cases where it holds. Finally, we prove a result on coalescence of instabilities for the cases $(n,p)=(1,2), (2,3)$, showing that it is false in general." @default.
- W4285429140 created "2022-07-15" @default.
- W4285429140 creator A5034355533 @default.
- W4285429140 date "2022-07-11" @default.
- W4285429140 modified "2023-09-23" @default.
- W4285429140 title "Isotypes of ICIS and images of deformations of map germs" @default.
- W4285429140 doi "https://doi.org/10.48550/arxiv.2207.05196" @default.
- W4285429140 hasPublicationYear "2022" @default.
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