A quadratic estimation for the Kühnel conjecture

The classical Heawood inequality states that if the complete graph $K_n$ on $n$ vertices is embeddable into the sphere with $g$ handles, then $g \ge(n-3)(n-4)/12$. Denote by $\Delta^k_n$ the union of $k$-faces of $n$-simplex. Denote by $S_g$ the connected sum of $g$ copies of the Cartesian product $S^k \times S^k$ of two $k$-dimensional spheres. A higher-dimensional analogue of the Heawood inequality is the Kühnel conjecture. In a simplified form it states that for every integer $k > 0$ there is $c_k > 0$ such that if $\Delta^k_n$ embeds into $S_g$, then $g > c_k n^{k+1}$. For $k > 1$ only linear estimates were known. We present a quadratic estimate $g > c_k n^2$. The proof is based on beautiful and fruitful interplay between geometric topology, combinatorics and linear algebra.

Планируется, что доклад будет частично доступен через Zoom (слайды должно быть видно хорошо, а доску — насколько позволит веб-камера ноутбука)
Подключение: https://mi-ras-ru.zoom.us/j/91599052030
Код доступа: эйлерова характеристика букета двух окружностей
(паролем является не приведённая фраза, а задаваемое ей число)