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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.

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    You can produce $\#$ with `$\#$`2012-03-08
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    my apologies...2012-03-08
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    @Jr., You should probably accept your own answer to this question or explain why it is unsatisfactory. Otherwise, if this stay without an accepted answer it will haunt us for ever! :)2012-05-07
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    What $\sharp$ means?2018-01-22

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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?

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    Yes, assuming $\mathbb P^2$ means $\mathbb P\#\mathbb P$.2012-03-08
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    It's not really clear what you were originally confused about, since you seemed to state the answer in your question.2012-03-08
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    @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