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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 $Pin(2)$-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:

   $$\array{ 2 D_{2n} &\overset{\phantom{AA}}{\hookrightarrow}& Pin_-(2) &\overset{\phantom{AA}}{\hookrightarrow}& Spin(3) \\ \big\downarrow &{}^{(pb)}& \big\downarrow &{}^{(pb)}& \big\downarrow \\ D_{2n} &\overset{\phantom{AA}}{\hookrightarrow}& O(2) &\overset{\phantom{AA}}{\hookrightarrow}& SO(3) }$$

   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 $Pin_{+}(2)$ group as well, I take it. Is either of them the default when $Pin(2)$ 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 $Pin_+(2)$, 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.

5. • CommentRowNumber5.
   • CommentAuthornLab edit announcer
   • CommentTimeJun 14th 2019
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   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