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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeFeb 13th 2019
   • PermaLink
   Author: Urs
   Format: MarkdownItexa minimum, for the moment just so as to record some references on $Pin(2)$-equivariant homotopy theory (as kindly pointed out by David Roberts) <a href="https://ncatlab.org/nlab/revision/Pin%282%29/1">v1</a>, <a href="https://ncatlab.org/nlab/show/Pin%282%29">current</a>

   a minimum, for the moment just so as to record some references on -equivariant homotopy theory (as kindly pointed out by David Roberts)

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeFeb 13th 2019
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded this little diagram: $$ \array{ 2 D_{2n} &\overset{\phantom{AA}}{\hookrightarrow}& Pin_-(2) &\overset{\phantom{AA}}{\hookrightarrow}& Spin(3) \\ \big\downarrow &{}^{(pb)}& \big\downarrow &{}^{(pb)}& \big\downarrow \\ D_{2n} &\overset{\phantom{AA}}{\hookrightarrow}& O(2) &\overset{\phantom{AA}}{\hookrightarrow}& SO(3) } $$ <a href="https://ncatlab.org/nlab/revision/Pin%282%29/1">v1</a>, <a href="https://ncatlab.org/nlab/show/Pin%282%29">current</a>

   added this little diagram:

   v1, current

3. • CommentRowNumber3.
   • CommentAuthorDavid_Corfield
   • CommentTimeFeb 13th 2019
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexThere's a $Pin_{+}(2)$ group as well, I take it. Is either of them the default when $Pin(2)$ is mentioned?

   There’s a group as well, I take it. Is either of them the default when is mentioned?

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeFeb 13th 2019
   • PermaLink
   Author: Urs
   Format: MarkdownItexYes, there is $Pin_+(2)$, obtained by changing the square of the reflection generator from $-1$ to +1. I focused on $Pin_-(2)$ just because that's the choice that fits into the story of the [[finite subgroups of SU(2)]]. But if anyone has the energy, it would be good to add discussion of $Pin_+(2)$, too.

   Yes, there is , obtained by changing the square of the reflection generator from to +1. I focused on just because that’s the choice that fits into the story of the finite subgroups of SU(2). But if anyone has the energy, it would be good to add discussion of , too.

5. • CommentRowNumber5.
   • CommentAuthornLab edit announcer
   • CommentTimeJun 14th 2019
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexadded a (very) brief explanation for why Pin(2)-equivariant things appear in topology, and a reference to Furuta's paper Arun Debray <a href="https://ncatlab.org/nlab/revision/diff/Pin%282%29/8">diff</a>, <a href="https://ncatlab.org/nlab/revision/Pin%282%29/8">v8</a>, <a href="https://ncatlab.org/nlab/show/Pin%282%29">current</a>

   added a (very) brief explanation for why Pin(2)-equivariant things appear in topology, and a reference to Furuta’s paper

   Arun Debray

   diff, v8, current