3 problems

Let $d$ and $q$ be positive integers. For a continuous map $f:S^{d-1}\to\mathbb{R}^d$ and a point $p\notin f(S^{d-1})$, define the winding number $W(f,p)\in\mathbb{Z}$ by the homol…

Realization conjecture. For any integers $n_1,n_2,n_3,n_4$ whose sum is odd, there exists an almost embedding $f:K_4\to\mathbb R^2$ such that

Let $\mathcal{A}^{\eta}_4(\eta,1)$ be the four-arm event at mesh size $\eta$, let $\nu_4^{\eta}$ be the four-arm IIC measure, and let $\tilde{\theta}_{\eta}$ be the winding number…