Geodesic
Semi-Coherence for Semianalytic Sets and Stratifications and Singularity Theory of Mappings on Stratifications
Journal of Singularities, Tome 13 (2015), pp. 42-56

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We consider the conditions on a local stratification \cV which ensure that the local singularity theory in the sense of Thom-Mather, such as finite determinacy, versal unfolding, and classification theorems and their topological versions apply either to mappings on the stratified set \cV or for an equivalence of mappings which preserve \cV in source or target for any of the categories: complex analytic, real analytic, or smooth. For such a stratification \cV, it is sufficient that the equivalence group be a "geometric subgroup of A or K", and this reduces to the structure of the module Derlog(\cV) of germs of vector fields on the ambient space which are tangent to \cV. In the holomorphic or real analytic categories, with holomorphic, resp. real analytic stratifications, we show the necessary conditions are satisfied.
DOI : 10.5427/jsing.2015.13c
Classification : :57N80, 58K40, 58K60, :32S05, 32S60, 58A35 
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     author = {James Damon},
     title = {Semi-Coherence for {Semianalytic} {Sets} and {Stratifications} and {Singularity} {Theory} of {Mappings} on {Stratifications}},
     journal = {Journal of Singularities},
     pages = {42--56},
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     volume = {13},
     year = {2015},
     doi = {10.5427/jsing.2015.13c},
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James Damon. Semi-Coherence for Semianalytic Sets and Stratifications and Singularity Theory of Mappings on Stratifications. Journal of Singularities, Tome 13 (2015), pp. 42-56. doi: 10.5427/jsing.2015.13c

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