论文标题
涂鸦和换向者身份
Doodles and commutator identities
论文作者
论文摘要
涂鸦是一系列沉浸式圆圈的集合，没有$ 2 $ -sphere中的三个交叉点。第二作者和P. tayler表明，涂鸦在自由群体中诱导换向者身份（换向者之间的身份）。在本文中，我们通过专注于具有适当的绞索系统和基本换向因子身份的涂鸦来更加仔细地观察这个想法。特别是我们表明，有色涂鸦的共同体类别与基本换向器身份的弱等效类别之间存在两者。
A doodle is a collection of immersed circles without triple intersections in the $2$-sphere. It was shown by the second author and P.~Tayler that doodles induce commutator identities (identities amongst commutators) in a free group. In this paper we observe this idea more closely by concentrating on doodles with proper noose systems and elementary commutator identities. In particular we show that there is a bijection between cobordism classes of colored doodles and weak equivalence classes of elementary commutator identities.
