On the fundamental groups of subelliptic varieties

Yuta Kusakabe

Published 2022-12-14Version 1

We show that the fundamental group of any smooth subelliptic variety is finite. Moreover, it is also proved that every finite group can be realized as the fundamental group of a smooth subelliptic variety. As a consequence, it follows that there exists a smooth subelliptic variety homotopy equivalent to the $n$-sphere if and only if $n>1$. This result can be considered as a negative answer to the algebraic version of Gromov's problem on the homotopy types of Oka manifolds.