Timeline for Lower dimensional Pin cobordisms

9 events

when toggle format	what		by	license	comment
Jun 25, 2014 at 21:32	vote	accept	Zitao Wang
Jun 25, 2014 at 21:32	vote	accept	Zitao Wang
Jun 25, 2014 at 21:32
Jun 25, 2014 at 20:46	comment	added	user43326		Each copie of $\Sigma ^nHZ/2$ can only contribute a single $Z/2$. However, there are many copies, and the number of copies is not said explicitely in Theorem 2.2 of "Structure of Spin Cobordism Ring". This is why you need to compare with the results for $\pi _*Mspin$
Jun 25, 2014 at 20:18	comment	added	Zitao Wang		Everything works fine up to dimension 10. In dimension 22, seems that we are able to get all factors except $\mathbb{Z}_2 \oplus \mathbb{Z}_2$, it is a bit weird that we get this factor, since it comes from $BO<8n+2>$ in dim 8n+2+i, $i \equiv 6 (8)$, and dim=22 does not lie in this category. $K(\mathbb{Z}_2,n)$ can only contribute a single $\mathbb{Z}_2$, so it cannot be $K(\mathbb{Z}_2,n)$.
Jun 25, 2014 at 20:11	history	edited	user43326	CC BY-SA 3.0	Improved formatting
Jun 25, 2014 at 17:19	comment	added	user43326		You are right, I edited the answer.
Jun 25, 2014 at 17:19	history	edited	user43326	CC BY-SA 3.0	Correction of typos pointed out below in a comment
Jun 25, 2014 at 17:15	comment	added	Zitao Wang		This helps, thanks. Also $bo<8n-2>$ should be $bo<8n+2>$, and $j_i > 1$ instead of $j_i \geq 1$ right? Otherwise you get 2=2=1+1 so that $bo<8>$ appears twice.
Jun 25, 2014 at 14:14	history	answered	user43326	CC BY-SA 3.0