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What is the braid word for the link L6n1

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2

$begingroup$

Please consider the link L6n1

Please note that such link is not the Borromean link L6a4.

I am trying to obtain the braid word for L6n1.

Using SnapPy with the following code

In[5]: L2=Link('L6n1')



In[6]: word2 = L2.braid_word(); word2

we obtain the output

Out[6]: [1, -2, 1, 2, -1, 2]

it is to say, the word is $$ {sigma_{{1}}}{sigma_{{2}}}^{-1}{sigma_{{1}}}{sigma_{{2}}}{sigma_{{1}}}^{-1}{sigma_{{2}}}$$

From other side in the paper https://arxiv.org/pdf/1104.5144.pdf

the braid word for L6n1 is given as

$$sigma_{{1}}sigma_{{2}}sigma_{{1}}sigma_{{2}}sigma_{{1}}sigma_{{2}} = (sigma_{{1}}sigma_{{2}})^ {3}$$

Then my question is: how to transform the first braid word in to the second braid world?

knot-theory quantum-computation braid-groups

share|cite|improve this question

edited Mar 15 at 11:19

Juan Ospina

asked Mar 12 at 15:01

Juan OspinaJuan Ospina

1,5791614

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  I misread your question. Sorry.
  $endgroup$
  – Arthur
  Mar 12 at 15:06
  

  
  
  
  

add a comment | 

2

$begingroup$

Please consider the link L6n1

Please note that such link is not the Borromean link L6a4.

I am trying to obtain the braid word for L6n1.

Using SnapPy with the following code

In[5]: L2=Link('L6n1')



In[6]: word2 = L2.braid_word(); word2

we obtain the output

Out[6]: [1, -2, 1, 2, -1, 2]

it is to say, the word is $$ {sigma_{{1}}}{sigma_{{2}}}^{-1}{sigma_{{1}}}{sigma_{{2}}}{sigma_{{1}}}^{-1}{sigma_{{2}}}$$

From other side in the paper https://arxiv.org/pdf/1104.5144.pdf

the braid word for L6n1 is given as

$$sigma_{{1}}sigma_{{2}}sigma_{{1}}sigma_{{2}}sigma_{{1}}sigma_{{2}} = (sigma_{{1}}sigma_{{2}})^ {3}$$

Then my question is: how to transform the first braid word in to the second braid world?

knot-theory quantum-computation braid-groups

share|cite|improve this question

edited Mar 15 at 11:19

Juan Ospina

asked Mar 12 at 15:01

Juan OspinaJuan Ospina

1,5791614

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  I misread your question. Sorry.
  $endgroup$
  – Arthur
  Mar 12 at 15:06
  

  
  
  
  

add a comment | 

$begingroup$

Please consider the link L6n1

Please note that such link is not the Borromean link L6a4.

I am trying to obtain the braid word for L6n1.

Using SnapPy with the following code

In[5]: L2=Link('L6n1')



In[6]: word2 = L2.braid_word(); word2

we obtain the output

Out[6]: [1, -2, 1, 2, -1, 2]

it is to say, the word is $$ {sigma_{{1}}}{sigma_{{2}}}^{-1}{sigma_{{1}}}{sigma_{{2}}}{sigma_{{1}}}^{-1}{sigma_{{2}}}$$

From other side in the paper https://arxiv.org/pdf/1104.5144.pdf

the braid word for L6n1 is given as

$$sigma_{{1}}sigma_{{2}}sigma_{{1}}sigma_{{2}}sigma_{{1}}sigma_{{2}} = (sigma_{{1}}sigma_{{2}})^ {3}$$

Then my question is: how to transform the first braid word in to the second braid world?

knot-theory quantum-computation braid-groups

share|cite|improve this question

edited Mar 15 at 11:19

Juan Ospina

asked Mar 12 at 15:01

Juan OspinaJuan Ospina

1,5791614

$endgroup$

In[5]: L2=Link('L6n1')



In[6]: word2 = L2.braid_word(); word2

Out[6]: [1, -2, 1, 2, -1, 2]

share|cite|improve this question

edited Mar 15 at 11:19

Juan Ospina

asked Mar 12 at 15:01

Juan OspinaJuan Ospina

1,5791614

share|cite|improve this question

edited Mar 15 at 11:19

Juan Ospina

asked Mar 12 at 15:01

Juan OspinaJuan Ospina

1,5791614

asked Mar 12 at 15:01

Juan OspinaJuan Ospina

1,5791614

asked Mar 12 at 15:01

Juan OspinaJuan Ospina

1,5791614