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 Dec 12 awarded Organizer Dec 12 revised Infinitely sheeted covering spaces! added tags Dec 12 suggested approved edit on Infinitely sheeted covering spaces! Nov 29 comment Compact surfaces and Fundamental Groups @JasonDeVito I am tempted to say that the Euler characteristic of the surface has to be zero, but I don't have a very strong argument?? Nov 29 comment Compact surfaces and Fundamental Groups @JasonDeVito: By $M\cong N$ do you mean their fundamental groups? Nov 29 comment Compact surfaces and Fundamental Groups @JasonDeVito I think it multiplies, but i am not sure exactly how? Can you elaborate? Nov 29 comment Compact surfaces and Fundamental Groups Projectiv space $RP(2)$ would be another example I think? Nov 29 awarded Commentator Nov 29 comment Compact surfaces and Fundamental Groups @JasonDeVito How would the Euler Characteristic help me in this case? Nov 29 revised Compact surfaces and Fundamental Groups added 22 characters in body Nov 29 comment Compact surfaces and Fundamental Groups @ Neal: Yea sorry, I should have been more careful! I am not looking just for an answer at all, I want to know how to get to the answer. But I am having trouble figuring out how to tackle this question, so any hints would be appreciated? Nov 29 asked Compact surfaces and Fundamental Groups Nov 28 comment Showing that $\lim_{x\rightarrow 0} \frac{1}{x}\int_0^x |\sin(1/y)| \mathrm{d} y \not=0$ Wouldn't the limit be exactly $\frac{2}{\pi}$? Oct 27 comment convergent series, sequences? Thanks! Both nice solutions! Oct 27 comment convergent series, sequences? Great, it worked out! Tanks! Oct 27 asked convergent series, sequences? Oct 26 comment Fundamental Group! Ok, so given that the adjunction space represents the connected sum of 4 tori, then the presentation group would be: $\langle \alpha_1, \beta_1,\dots, \alpha_4, \beta_4 : \alpha_1\beta_1\alpha_1^{-1}\beta_1^{-1},\dots, \alpha_4\beta_4\alpha_4^{-1}\beta_4^{-1} \rangle$ right? If this is correct, then I just need to have a better argument as to why that adjunction space is the connected sum of 4 tori?? Oct 26 comment Fundamental Group! I guess, my first problem is to see how exactly this adjunction space is giving us a genus 4 surface...I mean, I can see it intuitively it makes sense, but how to show it more rigorously? Oct 26 awarded Editor Oct 26 revised Fundamental Group! deleted 143 characters in body