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On real algebraic knots and links
Multi angle
Authors : Orevkov, Stepan (Author of the conference)
CIRM (Publisher )
14P25 - Topology of real algebraic varieties
CIRM (Publisher )
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Abstract :
I will present the following results on real algebraic spatial curves:
(1) (joint with Mikhalkin) Classification of smooth irreducible spatial real algebraic curves of genus 0 or 1 up to degree 6 up to rigid isotopy.
(2) (joint with Mikhalkin) Classification of smooth irreducible spatial real algebraic curves with maximal encomplexed writhe up to (not rigid yet) isotopy.
(3) Classification of smooth spatial real algebraic curves of genus 0 with two irreducible components up to degree 6 up to rigid isotopy, in particular, the first (as far as know) example of two spatial real algebraic curves which are isotopic, have equal degree, genus and encomplexed writhe of each irreducible component but not rigidly isotopic.
MSC Codes : (1) (joint with Mikhalkin) Classification of smooth irreducible spatial real algebraic curves of genus 0 or 1 up to degree 6 up to rigid isotopy.
(2) (joint with Mikhalkin) Classification of smooth irreducible spatial real algebraic curves with maximal encomplexed writhe up to (not rigid yet) isotopy.
(3) Classification of smooth spatial real algebraic curves of genus 0 with two irreducible components up to degree 6 up to rigid isotopy, in particular, the first (as far as know) example of two spatial real algebraic curves which are isotopic, have equal degree, genus and encomplexed writhe of each irreducible component but not rigidly isotopic.
14P25 - Topology of real algebraic varieties
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 21/09/2017 Conference Date : 20/09/2017 Subseries : Research talks arXiv category : Algebraic Geometry ; Geometric Topology Mathematical Area(s) : Topology ; Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Video Time : 00:57:37 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2017-09-20_Orevkov.mp4 
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Information on the Event
Event Title : Perspectives in real geometry / Perspectives en géométrie réelleEvent Organizers : Brugallé, Erwan ; Itenberg, Ilia ; Shustin, Eugenii Dates : 18/09/2017 - 22/09/2017 Event Year : 2017 Event URL : http://conferences.cirm-math.fr/1782.html
Citation Data
DOI : 10.24350/CIRM.V.19222603Cite this video as: Orevkov, Stepan (2017). On real algebraic knots and links. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19222603 URI : http://dx.doi.org/10.24350/CIRM.V.19222603 |
See Also
- [Post-edited] Expected topology of a random subcomplex in a simplicial complex / Author of the conference Welschinger, Jean-Yves.
- [Multi angle] Real curves and a Klein TQFT / Author of the conference Georgieva, Penka.
- [Multi angle] Sums of three squares and Noether-Lefschetz loci / Author of the conference Benoist, Olivier.
- [Multi angle] Complex torus, its good compactifications and the ring of conditions / Author of the conference Khovanskii, Askold.
Bibliography
- Mikhalkin, G., & Orevkov, S. (2016). Real algebraic knots and links of small degree. Journal of Knot Theory and its Ramifications, 25(12), Article ID 1642010 - http://dx.doi.org/10.1142/S0218216516420104
