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1. • CommentRowNumber1.
   • CommentAuthorSamuel Adrian Antz
   • CommentTimeMar 10th 2024
   • PermaLink
   Author: Samuel Adrian Antz
   Format: MarkdownItexCreated page for [[BO(n)]], the [[classifying space]] of the [[orthogonal group]] O(n). (See [discussion on Stiefel-Whitney class](https://nforum.ncatlab.org/discussion/3300/stiefelwhitney-class).) There is still a lot to add though. <a href="https://ncatlab.org/nlab/revision/BO%28n%29/1">v1</a>, <a href="https://ncatlab.org/nlab/show/BO%28n%29">current</a>

   Created page for BO(n), the classifying space of the orthogonal group O(n). (See discussion on Stiefel-Whitney class.) There is still a lot to add though.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorSamuel Adrian Antz
   • CommentTimeMar 10th 2024
   • (edited Mar 10th 2024)
   • PermaLink
   Author: Samuel Adrian Antz
   Format: MarkdownItexEdit: Accidently pushed the same message again. There seem to be some render issues needing to be fixed. Edit: They are fixed now.

   Edit: Accidently pushed the same message again. There seem to be some render issues needing to be fixed. Edit: They are fixed now.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMar 11th 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexGood. In the first sentence I have added a parenthetical making it read: > $B O(n)$ is the [[classifying space]] for ([[principal bundles]] with [[structure group]]) the [[orthogonal group]] $O(n)$. <a href="https://ncatlab.org/nlab/revision/diff/BO%28n%29/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/BO%28n%29/2">v2</a>, <a href="https://ncatlab.org/nlab/show/BO%28n%29">current</a>

   Good.

   In the first sentence I have added a parenthetical making it read:

   $B O(n)$ is the classifying space for (principal bundles with structure group) the orthogonal group $O(n)$.

   diff, v2, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeMar 11th 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded cross-link with *[[KO]]* <a href="https://ncatlab.org/nlab/revision/diff/BO%28n%29/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/BO%28n%29/2">v2</a>, <a href="https://ncatlab.org/nlab/show/BO%28n%29">current</a>

   added cross-link with KO

   diff, v2, current

5. • CommentRowNumber5.
   • CommentAuthorSamuel Adrian Antz
   • CommentTimeMar 11th 2024
   • PermaLink
   Author: Samuel Adrian Antz
   Format: MarkdownItexChanged "limit" to "colimit" and added [[stable orthogonal group]] like on [[BU(n)]]. <a href="https://ncatlab.org/nlab/revision/diff/BO%28n%29/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/BO%28n%29/3">v3</a>, <a href="https://ncatlab.org/nlab/show/BO%28n%29">current</a>

   Changed “limit” to “colimit” and added stable orthogonal group like on BU(n).

   diff, v3, current

6. • CommentRowNumber6.
   • CommentAuthorSamuel Adrian Antz
   • CommentTimeMar 12th 2024
   • (edited Mar 12th 2024)
   • PermaLink
   Author: Samuel Adrian Antz
   Format: MarkdownItexAdded the simplest classifying space $B O(1)\cong\mathbb{R}P^\infty$ and its classification of $O(1)$ [[principal bundles]]. (A section about the general classification will follow soon.) Also linked the Wikipedia page _[Classifying space for O(n)](https://en.wikipedia.org/wiki/Classifying_space_for_O(n))_. Edit: As a link including ")" can't be linked due to disrupting the <div>[....](....)</div> environment, I have created a redirect from "Classifying space for orthogonal group". <a href="https://ncatlab.org/nlab/revision/diff/BO%28n%29/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/BO%28n%29/4">v4</a>, <a href="https://ncatlab.org/nlab/show/BO%28n%29">current</a>

   Added the simplest classifying space $B O(1)\cong\mathbb{R}P^\infty$ and its classification of $O(1)$ principal bundles. (A section about the general classification will follow soon.) Also linked the Wikipedia page Classifying space for O(n).

   Edit: As a link including “)” can’t be linked due to disrupting the

   [….](….)

   environment, I have created a redirect from “Classifying space for orthogonal group”.

   diff, v4, current

7. • CommentRowNumber7.
   • CommentAuthorSamuel Adrian Antz
   • CommentTimeMar 12th 2024
   • PermaLink
   Author: Samuel Adrian Antz
   Format: MarkdownItexAdded reference for definition in Milnor & Stasheff. Added connection to [[characteristic classes]]. (I plan to create the page for [[balanced product]] in the future.) Also linked pages of [[BSO(n)]] and [[BSU(n)]], which I will create either today or tomorrow. <a href="https://ncatlab.org/nlab/revision/diff/BO%28n%29/5">diff</a>, <a href="https://ncatlab.org/nlab/revision/BO%28n%29/5">v5</a>, <a href="https://ncatlab.org/nlab/show/BO%28n%29">current</a>

   Added reference for definition in Milnor & Stasheff. Added connection to characteristic classes. (I plan to create the page for balanced product in the future.) Also linked pages of BSO(n) and BSU(n), which I will create either today or tomorrow.

   diff, v5, current