Discussion of Homotopy Type Theory and Univalent Foundations
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From: Dan Christensen <jdc@uwo.ca>
To: Homotopy Type Theory <HomotopyTypeTheory@googlegroups.com>
Subject: Re: [HoTT] Real Projective space (and other projective spaces too)
Date: Sat, 18 Aug 2018 10:45:59 -0400	[thread overview]
Message-ID: <874lfrhgwo.fsf@uwo.ca> (raw)
In-Reply-To: <e6d4c35e-a03b-41f5-b7d3-b7f6a63cba72@googlegroups.com> (Ali Caglayan's message of "Sat, 18 Aug 2018 07:30:19 -0700 (PDT)")

On Aug 18, 2018, Ali Caglayan <alizter@gmail.com> wrote:

> This screams to me an alternative definition for ℝℙⁿ (and maybe ℂℙⁿ,...)
>
> Inductive RP (n:ℕ) :=
> | map : Sⁿ -> RP n
> | glue : (x y:S⁰) -> map(in x) = map(in y)
>
> Where in : S⁰→Sⁿ is the obvious inclusion map.

That HIT would be S^n with four edges attached:  two edges connecting
the north pole to the south pole, and a self-loop at each pole.  So
homotopically it would be S^n wedged with a wedge of four circles.

To get the right space with the right bundle over it, see:

  The real projective spaces in homotopy type theory
  Ulrik Buchholtz, Egbert Rijke
  https://arxiv.org/abs/1704.05770

Dan

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  parent reply	other threads:[~2018-08-18 14:46 UTC|newest]

Thread overview: 6+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2018-08-18 14:30 Ali Caglayan
2018-08-18 14:33 ` [HoTT] " Ali Caglayan
2018-08-18 14:45 ` Dan Christensen [this message]
2018-08-18 16:17   ` [HoTT] " Guillaume Brunerie
2018-08-18 19:35     ` Dan Christensen
2018-08-19  6:36       ` Guillaume Brunerie

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