3 problems

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Acyclicity conjecture for components of line transversals
Acyclicity conjecture. Every connected component of the space of line transversals to $F$ is acyclic.
Conjectureopenconvexity topology transversal-geometryarXiv posted 3 days ago
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The dual Tverberg transversal conjecture for families with the $d-m$ -intersection property
The dual Tverberg transversal conjecture. There exist an $m$ -flat $L$ and, for every $i=0,ldots,m$ , $r_i$ pairwise disjoint nonempty subfamilies…
Conjectureopenconvexity transversal-geometry tverberg-type-theoremsarXiv posted 3 days ago
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The dual Tverberg conjecture for families with the $d$ -intersection property
The dual Tverberg conjecture. There exist a point $xinmathbb R^d$ and $r$ pairwise disjoint nonempty subfamilies $mathcal F_1,ldots,mathcal F_rsubseteqmathcal F$ such that, for eve…
Conjectureopenconvexity transversal-geometry tverberg-type-theoremsarXiv posted 3 days ago

Acyclicity conjecture for components of line transversals