Vanishing topology of codimension 1 multi-germs over R and C

1999/12/02 by Thomas M. Cooper, Thomas Cooper, Cooper, Thomas +5 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14B05 #msc:32S05 #msc:32S30

paper · pdf · doi:10.48550/arxiv.math/9912016

35 pages, 4 figures

arxiv created 1999/12/02 · arxiv updated 2009/11/30

Abstract

We construct all codimension 1 multi-germs of maps (kⁿ,T)-->(k^p,0) with n > p-2, (n,p) nice dimensions, k = R or C, by augmentation and concetenation operations, starting from mon-germs (|T|=1). As an application, we prove general results for multi-germs of corank <2: every one has a real form with real perturbation carrying the vanishing homology of the complexification, every one is quasihomogeneous, and when n=p-1 every one has image Milnor number equal to 1 (the comparable result for n>p-1 being already known).

Citations

• A and the vanishing topology of discriminants

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• Good real pictures of corank one map germs from the n-space to the (n+1)-space

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