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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJan 25th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexA stand-alone page, with a detailed proof/explanation for the lemma that $B \mathbb{K}^\times \overset{0}{\to} Th(\mathcal{L}^\ast_{B\mathbb{K}^\times})$ is a weak homotopy equialence. This was (and is) stated with the traditional sketchy proof on the page _[[universal complex orientation on MU]]_. This stand-alone page here since it's awkward to point to within that page just for this lemma, and also in order to generalize beyond the complex ground field and to have more room to talk about the proof. <a href="https://ncatlab.org/nlab/revision/zero-section+into+Thom+space+of+universal+line+bundle+is+weak+equivalence/1">v1</a>, <a href="https://ncatlab.org/nlab/show/zero-section+into+Thom+space+of+universal+line+bundle+is+weak+equivalence">current</a>

   A stand-alone page, with a detailed proof/explanation for the lemma that $B \mathbb{K}^\times \overset{0}{\to} Th(\mathcal{L}^\ast_{B\mathbb{K}^\times})$ is a weak homotopy equialence.

   This was (and is) stated with the traditional sketchy proof on the page universal complex orientation on MU. This stand-alone page here since it’s awkward to point to within that page just for this lemma, and also in order to generalize beyond the complex ground field and to have more room to talk about the proof.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJan 26th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded ([here](https://ncatlab.org/nlab/show/zero-section+into+Thom+space+of+universal+line+bundle+is+weak+equivalence#ViaContractibleInfiniteDimensionalSpheres)) to the first step of the proof the alternative argument via contractibility of the infinite sphere <a href="https://ncatlab.org/nlab/revision/diff/zero-section+into+Thom+space+of+universal+line+bundle+is+weak+equivalence/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/zero-section+into+Thom+space+of+universal+line+bundle+is+weak+equivalence/3">v3</a>, <a href="https://ncatlab.org/nlab/show/zero-section+into+Thom+space+of+universal+line+bundle+is+weak+equivalence">current</a>

   added (here) to the first step of the proof the alternative argument via contractibility of the infinite sphere

   diff, v3, current