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Poincaré-Reeb graphs of real algebraic domains

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Authors : Sorea, Miruna-Stefana (Author of the conference)
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 :
14P25 - Topology of real algebraic varieties
26Cxx - Polynomials, rational functions
58K05 - Critical points of functions and mappings
05E14 - Combinatorial aspects of algebraic geometry

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : 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

Information on the Event

Event Title : Real Algebraic Geometry / Géometrie algébrique réelle
Event 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.19978103
Cite 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

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