how do I find the presentation of the fundamental group of $\mathbb{P}^2\#\mathbb{T}$? I only know that it is a quotient of the free group of rank 4 by the least normal subgroup containing the elements of the form $\alpha_1^2 \alpha_2^2 \beta_1 \beta_2 \beta_1^{-1}\beta_2^{-1}$. Thanks.
Presentation of $\mathbb{P}^2 \#\mathbb{T}$
0
$\begingroup$
algebraic-topology
-
0What $\sharp$ means? – 2018-01-22
1 Answers
0
I think that answer is obvious: the free group of order 4 (generated by $a,b,c,d$) such that $a^2 b^2 c= dc d^{-1}$, am I right?
-
0@JimConant I think that the problem is what do I mean by "a presentation", after thinking about it, I remembered the definition. – 2012-03-08