Knotting of algebraic curves in complex surfaces



Knotting of algebraic curves in CP2
Finashin, Sergey (2002-01-01)
For any k⩾3, I construct infinitely many pairwise smoothly non-isotopic smooth surfaces homeomorphic to a non-singular algebraic curve of degree 2k, realizing the same homology class as such a curve and having abelian fundamental group ⧹ . This gives an answer to Problem 4.110 in the Kirby list (Kirby, Problems in low-dimensional topology, in: W. Kazez (Ed.), Geometric Topology, AMS/IP Stud. Adv. Math. vol 2.2, Amer. Math. Soc., Providence, 1997).
Knotted solutions of maxwell equations
Altun, Salman Eren.; Sarıoğlu, Bahtiyar Özgür; Department of Physics (2019)
We review Rañada’s knotted solutions of Maxwell equations in this thesis. We explain the method behind these constructions and its relation to topology. The method starts with the null field assumption. We obtain the initial conditions of the electromagnetic field using the Hopf map. Then we find the time-dependent fields using Fourier transformation techniques. Finally, we analyze the properties of general torus knotted solutions and show that these also include the non-null fields.
Invariant reduction of partially potential branching equations and iterative methods in the problem on a bifurcation point with a symmetry
Karasözen, Bülent (2004-03-01)
Coding algorithms for 3DTV - A survey
Smolic, Aljoscha; Mueller, Karsten; Stefanoski, Nikolce; Ostermann, Joern; Gotchev, Atanas; Akar, Gözde; Triantafyllidis, Georgios; Koz, Alper (2007-11-01)
Research efforts on 3DTV technology have been strengthened worldwide recently, covering the whole media processing chain from capture to display. Different 3DTV systems rely on different 3-D scene representations that integrate various types of data. Efficient coding of these data is crucial-for the success of 3DTV. Compression of pixel-type data including stereo video, multiview video, and associated depth or disparity maps extends available principles of classical video coding. Powerful algorithms and ope...
Exact solutions and the consistency of 3D minimal massive gravity
Altas, Emel; Tekin, Bayram (2015-07-20)
We show that all algebraic type-O, type-N and type-D and some Kundt-type solutions of topologically massive gravity are inherited by its holographically well-defined deformation, that is, the recently found minimal massive gravity. This construction provides a large class of constant scalar curvature solutions to the theory. We also study the consistency of the field equations both in the source-free and matter-coupled cases. Since the field equations of MMG do not come from a Lagrangian that depends on the...
Citation Formats
S. Finashin, “Knotting of algebraic curves in complex surfaces,” Turkish Journal of Mathematics, vol. 25, no. 1, pp. 147–158, 2001, Accessed: 00, 2021. [Online]. Available: