Timeline for Blocksum induces a unital H-space structure on the space of Fredholm operators

7 events

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Mar 1, 2019 at 13:11	history	edited	Eric Schlarmann	CC BY-SA 4.0	edited title
Mar 1, 2019 at 10:43	history	edited	Eric Schlarmann		edited tags
Mar 1, 2019 at 9:22	comment	added	Denis Nardin		@BenediktHunger I guess the question is whether the linear isometries operad (whose n-th space is given by the space of isometric embeddings of $H^{\oplus n}$ into $H$) is an $E_\infty$-operad, because it seems to me that the blocksum produces an action of this operad on $Fred(H)$. But, again, I haven't thought it through
Mar 1, 2019 at 5:25	comment	added	Benedikt Hunger		I do not think that Yoneda works here, since it is not clear that block sum induces addition over non-compact spaces, in particular over $Fred(H)$ itself.
Feb 28, 2019 at 18:26	history	edited	Eric Schlarmann	CC BY-SA 4.0	added 23 characters in body
Feb 28, 2019 at 17:53	comment	added	Denis Nardin		Well an abstract reason why it does exist is that $K^0(X)$ is an abelian group functorially in $X$, and so Yoneda forces the unit (and sum, and inverse) maps to exist. I suspect an explicit construction can be done along the line of the contraction of the identity of $S^∞$ but I'll confess not having thought it through
Feb 28, 2019 at 17:44	history	asked	Eric Schlarmann	CC BY-SA 4.0