5 problems

Proposed cohomological lower bound. If

For a group $Q$, let $K(Q,1)$ be a classifying space, and write ${\sf cat}(K(Q,1))$ for its Lusternik–Schnirelmann category. For a homomorphism $\phi\colon G\to H$, let…

Let $f\colon X\rightarrow Y$ be a map whose rationalisation $f_0$ admits a homotopy retraction. Let ${\rm secat}(f_0)$ denote the sectional category of the rationalisation and…

Let $(ambda V,d)$ be a Sullivan model of a rational space $X_0$, and let … be the kernel of the multiplication morphism. Jessup–Murillo–Parent conjecture. The rational topological…

Let $f:Y\rightarrow X$ be a map. A homotopy retraction of $f$ is a map $r:X\rightarrow Y$ such that $rf\simeq \operatorname{id}_Y$. The sectional category of $f$, denoted by…