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Fernando Oliveira
Fernando Oliveira
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Let $S_1$ and $S_2$ be two surfaces with compact boundary and the same number of boundary components. Let $M_1$ and $M_2$ be the surfaces obtained by glueing closed disks to the boundary of $S_1$ and $S_2$, respectively. Is there a direct proof that if $M_1$ and $M_2$ are homeomorphic then $S_1$ and $S_2$ are also homeomorphic? I know that this can be done in the compact case using normal forms, as in Massey's book. And if the surfaces are nonot compact?

Let $S_1$ and $S_2$ be two surfaces with compact boundary and $M_1$ and $M_2$ the surfaces obtained by glueing closed disks to the boundary of $S_1$ and $S_2$, respectively. Is there a direct proof that if $M_1$ and $M_2$ are homeomorphic then $S_1$ and $S_2$ are also homeomorphic? I know that this can be done in the compact case using normal forms, as in Massey's book. And if the surfaces are no compact?

Let $S_1$ and $S_2$ be two surfaces with compact boundary and the same number of boundary components. Let $M_1$ and $M_2$ be the surfaces obtained by glueing closed disks to the boundary of $S_1$ and $S_2$, respectively. Is there a direct proof that if $M_1$ and $M_2$ are homeomorphic then $S_1$ and $S_2$ are also homeomorphic? I know that this can be done in the compact case using normal forms, as in Massey's book. And if the surfaces are not compact?

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Fernando Oliveira
Fernando Oliveira
  • 37
  • 5

Let $S_1$ and $S_2$ be two surfaces with compact boundary and $M_1$ and $M_2$ the surfaces obtained by glueing closed disks to the boundary of $S_1$ and $S_2$, respectively. Is there a direct proof that if $M_1$ and $M_2$ are homeomorphic then $S_1$ and $S_2$ are also homeomorphic? I know that this can be done in the compact case using normal formforms, as in Massey's book. And if the surfaces are no compact?

Let $S_1$ and $S_2$ be two surfaces with compact boundary and $M_1$ and $M_2$ the surfaces obtained by glueing closed disks to the boundary of $S_1$ and $S_2$, respectively. Is there a direct proof that if $M_1$ and $M_2$ are homeomorphic then $S_1$ and $S_2$ are also homeomorphic? I know that this can be done in the compact case using normal form, as in Massey's book. And if the surfaces are no compact?

Let $S_1$ and $S_2$ be two surfaces with compact boundary and $M_1$ and $M_2$ the surfaces obtained by glueing closed disks to the boundary of $S_1$ and $S_2$, respectively. Is there a direct proof that if $M_1$ and $M_2$ are homeomorphic then $S_1$ and $S_2$ are also homeomorphic? I know that this can be done in the compact case using normal forms, as in Massey's book. And if the surfaces are no compact?

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Fernando Oliveira
Fernando Oliveira
  • 37
  • 5

Is it possible to prove that surfaces with compact boundary are homeomorphic by glueing disks to the boundary components?

Let $S_1$ and $S_2$ be two surfaces with compact boundary and $M_1$ and $M_2$ the surfaces obtained by glueing closed disks to the boundary of $S_1$ and $S_2$, respectively. Is there a direct proof that if $M_1$ and $M_2$ are homeomorphic then $S_1$ and $S_2$ are also homeomorphic? I know that this can be done in the compact case using normal form, as in Massey's book. And if the surfaces are no compact?