日時：2026年6月2日（火），15:00-16:30
場所：理学部A202号室
講師：Emmanuel Graff 氏 (The university of Tokyo)
題目：The homotopy braid group is torsion-free
In the Kourovka Notebook, V. Lin asked whether there exists a non-trivial epimorphism from the braid group onto a non-abelian torsion-free group. The homotopy braid group, introduced by D. L. Goldsmith in 1974, naturally emerged as a promising candidate. In 2001, S. P. Humphries proved that this group is torsion-free for fewer than six strands.
In this talk, we present a new approach based on the broader framework of welded braids together with algebraic techniques, leading to a proof that the homotopy braid group is torsion-free in full generality. As a consequence, the homotopy braid group provides a complete answer to Lin’s question.