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Poincaré-Reeb graphs of real algebraic domains
Multi angle
Authors : Sorea, Miruna-Stefana (Author of the conference)
CIRM (Publisher )
14P25 - Topology of real algebraic varieties
26Cxx - Polynomials, rational functions
58K05 - Critical points of functions and mappings
05E14 - Combinatorial aspects of algebraic geometry
CIRM (Publisher )
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Abstract :
A real algebraic domain is a closed topological subsurface of a real affine plane such that its boundary consists of disjoint smooth connected components of real algebraic plane curves. Our goal is to study the nonconvexity of real algebraic domains relative to the vertical direction. To this end, we collapse all vertical segments contained in the algebraic domain, yielding a Poincar´e–Reeb graph which is naturally transversal to the foliation by vertical lines. Our main result is the following: any transversal graph whose vertices have only valencies 1 and 3 and are situated on distinct vertical lines arises up to isomorphism as a Poincar´e–Reeb graph of a real algebraic domain. We also give a purely topological description of the setting in which our construction of Poincar´e–Reeb graphs may be applied, with no differentiability assumptions. This is a joint work with Arnaud Bodin and Patrick Popescu-Pampu (Université de Lille, France).
Keywords : combinatorial type; Morse theory; Poincaré–Reeb graph; real algebraic curve; real polynomial functions
MSC Codes : Keywords : combinatorial type; Morse theory; Poincaré–Reeb graph; real algebraic curve; real polynomial functions
14P25 - Topology of real algebraic varieties
26Cxx - Polynomials, rational functions
58K05 - Critical points of functions and mappings
05E14 - Combinatorial aspects of algebraic geometry
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 18/11/2022 Conference Date : 25/10/2022 Subseries : Research talks arXiv category : Group Theory Mathematical Area(s) : Topology Format : MP4 (.mp4) - HD Video Time : 00:58:34 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2022-10-25_Sorea.mp4 
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Information on the Event
Event Title : Real Algebraic Geometry / Géometrie algébrique réelleEvent Organizers : Bihan, Frédéric ; Brugallé, Erwan ; Dickenstein, Alicia ; Dutertre, Nicolas Dates : 24/10/2022 - 28/10/2022 Event Year : 2022 Event URL : https://conferences.cirm-math.fr/2626.html
Citation Data
DOI : 10.24350/CIRM.V.19978103Cite this video as: Sorea, Miruna-Stefana (2022). Poincaré-Reeb graphs of real algebraic domains. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19978103 URI : http://dx.doi.org/10.24350/CIRM.V.19978103 |
See Also
- [Multi angle] Random algebraic geometry - lecture 4 / Author of the conference Lerario, Antonio.
- [Multi angle] Random algebraic geometry - lecture 3 / Author of the conference Lerario, Antonio.
- [Multi angle] Random algebraic geometry - lecture 2 / Author of the conference Lerario, Antonio.
- [Multi angle] Random algebraic geometry - lecture 1 / Author of the conference Lerario, Antonio.
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