1
$\begingroup$

Let $A$ be open, connected set in $\mathbb{C}$. We know that if a $\alpha$ loop is null-homotopic in $A$ then it is null-homolog. Is the converse true?

  • 0
    I don't know the answer for open, connected subsets of $\mathbb{C}$, but in general, the answer is no. See, for example, the Poincare dodecahedral space.2012-11-06

0 Answers 0