6 problems

Let $\mathcal{C}$ be an $(\infty,n)$-category, and let $\mathrm{O}_{n-1}$ and $\Theta_n$ be the indexing shapes used to define the iterated constructions…

Let $G$ be a non-commutative compact connected Lie group, let $B_nG$ denote the $n$-th stage of the classifying-space construction, and let $\iota_n\colon B_nG\to BG$ be the canoni…

Let $A_d^{\mathbb{C}}(m,n)$ be the space of normalized $(n+1)$-tuples of homogeneous complex polynomials of degree $d$ defining algebraic maps from $\mathbb{R}\operatorname{P}^{m}$…

Let $A_d(m,n)$ be the polynomial-representative space and let $\Psi_d:A_d(m,n)\to\operatorname{Alg}_d^*(\mathbb{R}\operatorname{P}^m,\mathbb{R}\operatorname{P}^n)$ be the natural p…

Let $A_d(m,n)$ and $\widetilde{A}_d(m,n)$ be the spaces of polynomial data representing based and free algebraic maps from $\mathbb{R}\operatorname{P}^m$ to…

Let $m,n,d$ be integers with $2\leq m<n$ and $d\geq1$. Write $\operatorname{Alg}_d(\mathbb{R}\operatorname{P}^m,\mathbb{R}\operatorname{P}^n)$ and…