5 problems

Bullett's modular Mandelbrot mating conjecture
arXiv@arxiv
Bullett's conjecture. For all parameters $a$ in the modular Mandelbrot set, the correspondence $F_a$ is a mating between a quadratic polynomial with connected Julia set and…
Conjecturesolvedcomplex-dynamics holomorphic-correspondences matings
0
Bullett–Penrose conjecture on mating polynomials with Hecke groups
arXiv@arxiv
Let $f$ be a complex polynomial with connected Julia set, and let the corresponding Hecke group be the Fuchsian group associated with the degree of $f$ . Bullett–Penrose conjecture.…
Conjectureopencomplex-dynamics holomorphic-correspondences kleinian-groups
0
Holomorphic Lefschetz formula for transversal correspondences
arXiv@arxiv
Holomorphic Lefschetz conjecture for correspondences. The displayed formula holds. This is intended as the correspondence analogue of the holomorphic Lefschetz fixed point formula,…
Conjectureopencomplex-geometry fixed-point-theorems holomorphic-correspondences
0
Carpet conjecture for filled Julia sets in the intermediate connectedness locus
arXiv@arxiv
Carpet conjecture. For every $c\in M_{\beta}\setminus M_{\beta,0}$ , the filled Julia set $K_c$ is a Carpet.
Conjectureopencomplex-dynamics holomorphic-correspondences julia-sets
0
The Mandelbrot homeomorphism conjecture for modular matings
arXiv@arxiv
Mandelbrot homeomorphism conjecture. The Mandelbrot set $M$ is homeomorphic to $M_{\Gamma}$ . The family $\mathcal{F}_a$ has been shown to mate parabolic quadratic maps with…
Conjectureopencomplex-dynamics holomorphic-correspondences mandelbrot-set
1

5 problems

Bullett's modular Mandelbrot mating conjecture

Bullett–Penrose conjecture on mating polynomials with Hecke groups

Holomorphic Lefschetz formula for transversal correspondences

Carpet conjecture for filled Julia sets in the intermediate connectedness locus

The Mandelbrot homeomorphism conjecture for modular matings