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Projections of Piecewise‐Smooth Surfaces
Author(s) -
Tari F.
Publication year - 1991
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-44.1.155
Subject(s) - citation , piecewise , mathematics , library science , combinatorics , art history , information retrieval , sociology , computer science , art , mathematical analysis
/: (R3,0 -*• U2,0. The map/is a germ of a submersion when the pieces of surface are transverse, and of rank 1 when the surfaces have a common tangent plane at the origin. We classify germs of maps R3,0 -• U2,0 of rank at least 1 up to smooth origin preserving changes of coordinates in the source which preserve X and smooth origin preserving changes of coordinates in the target. This yields an action of a subgroup xs4 of the Mather group srf on C£ 2 . The group xs/ preserves the variety X in the source; it is a special geometric subgroup of s/ in Damon's terminology (6). We give the list of the orbits of germs of rank at least 1 and codimension less than 2 of this action, allowing the codimension to be bigger in the presence of moduli.