From: Ali Caglayan <alizter@gmail.com>
To: Homotopy Type Theory <HomotopyTypeTheory@googlegroups.com>
Subject: [HoTT] Re: Weaker Freudenthal
Date: Sun, 4 Aug 2019 03:43:41 -0700 (PDT) [thread overview]
Message-ID: <a4549eab-f563-42ad-a95a-10166e8e0664@googlegroups.com> (raw)
In-Reply-To: <81b245ba-e70f-4a13-8d0c-4eaad69f3da8@googlegroups.com>
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Here is an observation I had made:
We have that A is k-connected, we can show that susp A is (k+1)-connected
and then show that loop susp A is k-connected. This gives us a k-connected
map A -> 1 and a k-connected map loop susp A -> 1. This gives us a diagram
which commutes with A and loop susp A in the top corners and 1 in the
bottom. The LHS composition is homotopic to the RHS composition hence
naming eta : A -> loop susp A, we have eta o unitmap being k-connected
hence eta must also be k-connected. This isn't quite there.
Now I was hoping to use the fact that loop spaces are pullbacks hence there
are maps coming out of 1s hence (k+1)-connectedness appears, but I couldn't
get it to work.
On Sunday, 4 August 2019 12:59:09 UTC+3, Ali Caglayan wrote:
>
> Can we prove that the map A -> loop susp A is (k+1)-connected for a
> k-connected A, without having to invoke Freudenthal?
>
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prev parent reply other threads:[~2019-08-04 10:43 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
2019-08-04 9:59 [HoTT] " Ali Caglayan
2019-08-04 10:43 ` Ali Caglayan [this message]
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