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j0equ1nn
j0equ1nn
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Specifically, I am looking for a proof that for squarefree $d\in\mathbb{N}\setminus\{ 1,3\}$, there exists some Kleinian $\Gamma$ and some $\alpha\in$Aut$(PSL(2,\mathbb{Z})$$(PSL(2,\mathbb{Z}))$, such that the Bianchi group $\Gamma_d\cong \Gamma*_{\alpha}$. I have a reference that this proof appears in the article:

Charles Frohman and Benjamin Fine, "The amalgam structure of the Bianchi groups," 1986, Compte Rendu RSC Mathematiques, Volume 8, pp. 353-356.

But I cannot find access to this anywhere (at my university library, through Jstore, or anywhere else online). I did find an article on something very similar, by the same authors where they discuss amalgamated products instead. If I had to, iI could probably go through that and alter the argument appropriately, but I expect it would take me more time than I can spare right now. Here is the info on the similar article in case that's useful:

Charles Frohman and Benjamin Fine, "Some Amalgam Structures for Bianchi Groups," 1988, Proceedings of the American Mathematical SocietyProceedings of the American Mathematical Society, Vol. 102, No. 2, pp. 221-229

From reading that and some similar things, I expect the approach would involve looking at finite-cover manifolds of the Bianchi groups, and finding incompressible embeddings of the totally real half-plane into them, but I'm lost on the details.

Specifically, I am looking for a proof that for squarefree $d\in\mathbb{N}\setminus\{ 1,3\}$, there exists some Kleinian $\Gamma$ and some $\alpha\in$Aut$(PSL(2,\mathbb{Z})$, such that the Bianchi group $\Gamma_d\cong \Gamma*_{\alpha}$. I have a reference that this proof appears in the article:

Charles Frohman and Benjamin Fine, "The amalgam structure of the Bianchi groups," 1986, Compte Rendu RSC Mathematiques, Volume 8, pp. 353-356.

But I cannot find access to this anywhere (at my university library, through Jstore, or anywhere else online). I did find an article on something very similar, by the same authors where they discuss amalgamated products instead. If I had to, i could probably go through that and alter the argument appropriately, but I expect it would take me more time than I can spare right now. Here is the info on the similar article in case that's useful:

Charles Frohman and Benjamin Fine, "Some Amalgam Structures for Bianchi Groups," 1988, Proceedings of the American Mathematical Society, Vol. 102, No. 2, pp. 221-229

From reading that and some similar things, I expect the approach would involve looking at finite-cover manifolds of the Bianchi groups, and finding incompressible embeddings of the totally real half-plane into them, but I'm lost on the details.

Specifically, I am looking for a proof that for squarefree $d\in\mathbb{N}\setminus\{ 1,3\}$, there exists some Kleinian $\Gamma$ and some $\alpha\in$Aut$(PSL(2,\mathbb{Z}))$, such that the Bianchi group $\Gamma_d\cong \Gamma*_{\alpha}$. I have a reference that this proof appears in the article:

Charles Frohman and Benjamin Fine, "The amalgam structure of the Bianchi groups," 1986, Compte Rendu RSC Mathematiques, Volume 8, pp. 353-356.

But I cannot find access to this anywhere (at my university library, through Jstore, or anywhere else online). I did find an article on something very similar, by the same authors where they discuss amalgamated products instead. If I had to, I could probably go through that and alter the argument appropriately, but I expect it would take me more time than I can spare right now. Here is the info on the similar article in case that's useful:

Charles Frohman and Benjamin Fine, "Some Amalgam Structures for Bianchi Groups," 1988, Proceedings of the American Mathematical Society, Vol. 102, No. 2, pp. 221-229

From reading that and some similar things, I expect the approach would involve looking at finite-cover manifolds of the Bianchi groups, and finding incompressible embeddings of the totally real half-plane into them, but I'm lost on the details.

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j0equ1nn
j0equ1nn
  • 2.4k
  • 18
  • 29

Frohman & Fine's proof about Bianchi groups as HNN extensions (or anyone else's)

Specifically, I am looking for a proof that for squarefree $d\in\mathbb{N}\setminus\{ 1,3\}$, there exists some Kleinian $\Gamma$ and some $\alpha\in$Aut$(PSL(2,\mathbb{Z})$, such that the Bianchi group $\Gamma_d\cong \Gamma*_{\alpha}$. I have a reference that this proof appears in the article:

Charles Frohman and Benjamin Fine, "The amalgam structure of the Bianchi groups," 1986, Compte Rendu RSC Mathematiques, Volume 8, pp. 353-356.

But I cannot find access to this anywhere (at my university library, through Jstore, or anywhere else online). I did find an article on something very similar, by the same authors where they discuss amalgamated products instead. If I had to, i could probably go through that and alter the argument appropriately, but I expect it would take me more time than I can spare right now. Here is the info on the similar article in case that's useful:

Charles Frohman and Benjamin Fine, "Some Amalgam Structures for Bianchi Groups," 1988, Proceedings of the American Mathematical Society, Vol. 102, No. 2, pp. 221-229

From reading that and some similar things, I expect the approach would involve looking at finite-cover manifolds of the Bianchi groups, and finding incompressible embeddings of the totally real half-plane into them, but I'm lost on the details.