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On Generic Composites of Maps
Author(s) -
Montaldi James
Publication year - 1991
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/23.1.81
Subject(s) - submanifold , mathematics , manifold (fluid mechanics) , euclidean space , euclidean geometry , space (punctuation) , pure mathematics , topology (electrical circuits) , geometry , mathematical analysis , combinatorics , computer science , mechanical engineering , engineering , operating system
We show that (in the nice dimensions) if a stable map is restricted to a generic submanifold of the source manifold, then the resulting map will also be stable. At the same time, the analogous result for versal unfoldings is proved. A few examples of applications to the extrinsic geometry of submanifolds of Euclidean space are discussed.