Connected sum, Euler characteristic and homeomorphism

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Given the topological connected and compact surfaces $S_1$ and $S_2$ is it true that
$$ chi(S_1)=chi(S_2)=-18 implies S_1, S_2 mbox homeomorphic?$$



I know that the converse is always true, but in this case I don't know how to proceed.



Have you any book references which explain this or any help on how to justify the correctness or not of the statement?






general-topology surfaces







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  • From a different question that you asked this hour I conclude that you consider only connected and compact surfaces without boundary. In that case there's the following Hint. Simply consult the classification of closed surfaces to find out which ones have Euler characteristic -18.
    – Sofie Verbeek
    Aug 30 at 9:31










  • Actually "without boundaries" is not a hypothesis of the problem.
    – Phi_24
    Aug 30 at 9:56














up vote
0
down vote

favorite












Given the topological connected and compact surfaces $S_1$ and $S_2$ is it true that
$$ chi(S_1)=chi(S_2)=-18 implies S_1, S_2 mbox homeomorphic?$$



I know that the converse is always true, but in this case I don't know how to proceed.



Have you any book references which explain this or any help on how to justify the correctness or not of the statement?






general-topology surfaces







share|cite|improve this question























  • From a different question that you asked this hour I conclude that you consider only connected and compact surfaces without boundary. In that case there's the following Hint. Simply consult the classification of closed surfaces to find out which ones have Euler characteristic -18.
    – Sofie Verbeek
    Aug 30 at 9:31










  • Actually "without boundaries" is not a hypothesis of the problem.
    – Phi_24
    Aug 30 at 9:56












up vote
0
down vote

favorite









up vote
0
down vote

favorite











Given the topological connected and compact surfaces $S_1$ and $S_2$ is it true that
$$ chi(S_1)=chi(S_2)=-18 implies S_1, S_2 mbox homeomorphic?$$



I know that the converse is always true, but in this case I don't know how to proceed.



Have you any book references which explain this or any help on how to justify the correctness or not of the statement?






general-topology surfaces







share|cite|improve this question















Given the topological connected and compact surfaces $S_1$ and $S_2$ is it true that
$$ chi(S_1)=chi(S_2)=-18 implies S_1, S_2 mbox homeomorphic?$$



I know that the converse is always true, but in this case I don't know how to proceed.



Have you any book references which explain this or any help on how to justify the correctness or not of the statement?






general-topology surfaces




general-topology surfaces






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 30 at 7:36









Christoph

10.9k1240




10.9k1240










asked Aug 30 at 7:32









Phi_24

675




675











  • From a different question that you asked this hour I conclude that you consider only connected and compact surfaces without boundary. In that case there's the following Hint. Simply consult the classification of closed surfaces to find out which ones have Euler characteristic -18.
    – Sofie Verbeek
    Aug 30 at 9:31










  • Actually "without boundaries" is not a hypothesis of the problem.
    – Phi_24
    Aug 30 at 9:56
















  • From a different question that you asked this hour I conclude that you consider only connected and compact surfaces without boundary. In that case there's the following Hint. Simply consult the classification of closed surfaces to find out which ones have Euler characteristic -18.
    – Sofie Verbeek
    Aug 30 at 9:31










  • Actually "without boundaries" is not a hypothesis of the problem.
    – Phi_24
    Aug 30 at 9:56















From a different question that you asked this hour I conclude that you consider only connected and compact surfaces without boundary. In that case there's the following Hint. Simply consult the classification of closed surfaces to find out which ones have Euler characteristic -18.
– Sofie Verbeek
Aug 30 at 9:31




From a different question that you asked this hour I conclude that you consider only connected and compact surfaces without boundary. In that case there's the following Hint. Simply consult the classification of closed surfaces to find out which ones have Euler characteristic -18.
– Sofie Verbeek
Aug 30 at 9:31












Actually "without boundaries" is not a hypothesis of the problem.
– Phi_24
Aug 30 at 9:56




Actually "without boundaries" is not a hypothesis of the problem.
– Phi_24
Aug 30 at 9:56















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