7 problems

Let … be the exact sequence in the smooth case of Main Theorem 1.4. The even-l splitting conjecture. This exact sequence splits also when $l$ is even. The source explains that prov…

Let $W_{k,i,j}^{0alpha_1,0alpha_1+0alpha_2}=U(0\overline{\mathfrak{n}}[\hat{\nu}])\cdot v_{k,i,j}$, where … and $0\leq i,j\leq k$ with $i+j\leq k$. For $j=0$, these are the spaces…

Let $\mathcal{A}=\mathcal{H}/(\zeta^{\mathfrak{m}}(2))$, with depth-graded pieces $gr_r^{\mathfrak{D}}\mathcal{A}$, and let $\mathbb{P}^{\vee}$ be the weight-dual of the restricted…

For each $r\geq 3$, let $gr_r^{\mathfrak{D}}\mathcal{A}^{odd}$ denote the depth-graded totally odd part modulo $\zeta^{\mathfrak{m}}(2)$, let $\mathbb{P}^{\vee}$ be the weight-dual…

Compatibility conjecture. The two previous isomorphisms should be chosen so that the Gysin exact sequence and the Connes exact sequence are isomorphic. The claim proposes a compati…

Split exactness conjecture. This sequence, obtained by cutting the long exact $0$-$e$-$2$ sequence, is split exact for every $n\geq3$ and every $d$.

Gysin–Connes compatibility conjecture. The two isomorphisms can be chosen so that the Gysin exact sequence for $S^1$-equivariant symplectic homology and the Connes exact sequence a…