Re: [HoTT] What is knot in HOTT?

["José Manuel Rodriguez Caballero" <josephcmac@gmail.com>]

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Maybe the connection between knots and primes can be stated in terms of SL(2,R) and SL(2,Z), because these groups are essential in number theory, e.g., modular forms, quadratic forms.

José M


> On Jul 19, 2018, at 2:38 PM, Egbert Rijke <e.m.rijke@gmail.com> wrote:
> 
> Just for the record, a trivial but nice observation: the unknot is the representation of S3 as the join of S1 with itself:
> 
>            p2
> S1 x S1 ------> S1
>    |            |
>    | p1         |
>    V            V
>   S1 ---------> S3
> 
> Unfortunately, no-one has studied SL(2,R) and SL(2,Z) in HoTT yet. Although a trival way to obtain them is through cohesive HoTT would be nice if it were possible to define these spaces directly as higher inductive types.
> 
> Best,
> Egbert
> 
>> On Thu, Jul 19, 2018 at 1:56 PM, Daniel R. Grayson <danielrichardgrayson@gmail.com> wrote:
>> Quillen identified the complement of the trefoil knot with SL(2,R)/SL(2,Z), and the proof is
>> on page 84 of Milnor's book "Introduction to algebraic K-theory".
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> 
> 
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