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Jul 5 at 9:17 comment added Mark Grant An example which fits into your framework is the symmetric square $SP^2(\Sigma)$ of an orientable surface $\Sigma$ (the quotient of $\Sigma\times\Sigma$ by the involution that swaps factors). I'd be surprised if it's LS-category was unknown.
Jul 5 at 2:33 history became hot network question
Jul 4 at 19:43 answer added Mark Grant timeline score: 2
Jul 4 at 18:52 history edited LSpice CC BY-SA 4.0
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S Jul 4 at 18:30 review First questions
Jul 4 at 19:10
S Jul 4 at 18:30 history asked DavidChi CC BY-SA 4.0