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Baptiste Calmès
Baptiste Calmès
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I'm looking for a detailed reference about connected sums. I'd like it to contain a proof that a connected sum of connected surfaces is independent - up to homeomorphism - of the various choices involved in the process. There are several books in which it is stated, but I cannot find one in which it is proved. In particular, I do not see a simple argument implying that changing the orientation of the circle in the glueing has no influence on the homeomorphism class of the surface. I'm aware that for compact surfaces, this point more or less follows from the classification, but then what about non compact ones?

Any suggestion?

I'm looking for a detailed reference about connected sums. I'd like it to contain a proof that a connected sum of surfaces is independent - up to homeomorphism - of the various choices involved in the process. There are several books in which it is stated, but I cannot find one in which it is proved. In particular, I do not see a simple argument implying that changing the orientation of the circle in the glueing has no influence on the homeomorphism class of the surface. I'm aware that for compact surfaces, this point more or less follows from the classification, but then what about non compact ones?

Any suggestion?

I'm looking for a detailed reference about connected sums. I'd like it to contain a proof that a connected sum of connected surfaces is independent - up to homeomorphism - of the various choices involved in the process. There are several books in which it is stated, but I cannot find one in which it is proved. In particular, I do not see a simple argument implying that changing the orientation of the circle in the glueing has no influence on the homeomorphism class of the surface. I'm aware that for compact surfaces, this point more or less follows from the classification, but then what about non compact ones?

Any suggestion?

Source Link
Baptiste Calmès
Baptiste Calmès
  • 778
  • 5
  • 14

Connected sum of surfaces

I'm looking for a detailed reference about connected sums. I'd like it to contain a proof that a connected sum of surfaces is independent - up to homeomorphism - of the various choices involved in the process. There are several books in which it is stated, but I cannot find one in which it is proved. In particular, I do not see a simple argument implying that changing the orientation of the circle in the glueing has no influence on the homeomorphism class of the surface. I'm aware that for compact surfaces, this point more or less follows from the classification, but then what about non compact ones?

Any suggestion?