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| Author(s): |
Amanda Dias Falqueto
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) |
| Defense date: | 2023-02-16 |
| Examining board members: |
Farid Tari;
João Carlos Ferreira Costa;
Nivaldo de Góes Grulha Junior;
Bruna Oréfice Okamoto
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| Advisor: | Farid Tari |
| Abstract | |
The aim of this work is to study the local singularities of germs of k-folds for k 3 and derive from them hidden symmetries of curves in the Euclidean plane. We used the Complete Transversal Method in order to classify the A -simple singularities of map-germs C,0 C 2 ,0. We then prove that all the simple singularities of such germs can be realised by k-folding maps and that any k-folding map-germ can have an A -simple singularity. This does not occur in the case of surfaces, as proved in (PEÑAFORT SANCHIS; TARI, 2023). Finally, we proved that the singularities of k-folding map-germs reveal information about the local symmetry of the curve. (AU) | |
| FAPESP's process: | 21/02932-4 - On k-folding map-germs and hidden symmetries of curves in the Euclidean plane |
| Grantee: | Amanda Dias Falqueto |
| Support Opportunities: | Scholarships in Brazil - Master |