2011/10/10 by Aasa Feragen, Feragen, Aasa, Andrew Du Plessis +2 · 1 citation
Computer Science · Mathematics · #22F50 #58K70 #Coding theory and cryptography #Differential Geometry (math.DG) #FOS: Mathematics #Finite Group Theory Research #Rings, Modules, and Algebras #math.DG #msc:22F50 #msc:58K70
paper · pdf · doi:10.48550/arxiv.1110.1981
24 pages, 1 figure
arxiv created 2011/10/10 · openalex publication_date 2011/10/10 · arxiv updated 2011/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the structure of classical groups of equivalences for smooth multigerms f \colon (N,S) → (P,y), and extend several known results for monogerm equivalences to the case of mulitgerms. In particular, we study the group \A of source- and target diffeomorphism germs, and its stabilizer \Af. For monogerms f it is well-known that if f is finitely \A-determined, then \Af has a maximal compact subgroup MC(\Af), unique up to conjugacy, and \Af/MC(\Af) is contractible. We prove the same result for finitely \A-determined multigerms f. Moreover, we show that for a ministable multigerm f, the maximal compact subgroup MC(\Af) decomposes as a product of maximal compact subgroups MC(\Agi) for suitable representatives gi of the monogerm components of f. We study a product decomposition of MC(\Af) in terms of MC(\mathscrRf) and a group of target diffeomorphisms, and conjecture a decomposition theorem. Finally, we show that for a large class of maps, maximal compact subgroups are small and easy to compute.