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Guoqi Yan

Publications and source records attributed to Guoqi Yan.

6 recordsLinked to original sources
arXiv2026

Maximal compatibility of disklike $G$-transfer systems

Transfer systems are a combinatorial model for $N_{\infty}$-operads, which encode commutative structures in equivariant homotopy theory. Blumberg--Hill and Chan gave criteria for when two transfer systems are a compatible pair, meaning they encode the additive transfers and multiplicative norms of a ring-type structure. In this paper, given a transfer system encoding an additive structure, we give explicit formulae for the maximal transfer system it is compatible with. Our formulae simplify for disklike transfer systems, which typically encode additive structures. Further, we prove that (maximal) compatibility is functorial with respect to the inflation map induced by a quotient of groups, letting us compute maximal compatible transfer systems as inflations of connected transfer systems.

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arXiv2025

Real Global Group Laws and Hu-Kriz Maps

Recently, Hausmann defined global group laws and used them to prove that $MU^G_*$ is the $G$-equivariant Lazard ring, for $G$ a compact abelian Lie group. On the other hand, Hu and Kriz showed that the restriction map induces an isomorphism $M \mathbb{R}^{C_2}_{\rho *} \cong MU_{2*}$. In this paper, we blend these stories. We utilize the $C_2$-global spectrum $\mathbf{MR}$ defined by Schwede in an unpublished note, which gives rise to a genuine $G$-spectrum $M \mathbb{R}_\eta$ for each augmented compact Lie groups $\eta: G\to C_2$, simultaneously generalizing $MU_G$ and $M \mathbb{R}$. In the case of semi-direct product augmentations $G \rtimes C_2\to C_2$ with $G$ compact abelian Lie and $C_2$ acting by inversion, we show that the restriction along the inclusion $G \subset G \rtimes C_2$ is a split surjection $M \mathbb{R}^{G \rtimes C_2}_{\rho *} \rightarrow MU^{G}_{2*}$. Additionally, we propose an evenness conjecture, which implies that this map is an isomorphism. Along the way, we define Real $\eta$-orientations, Real global orientations, and corresponding notions of equivariant and global group laws.

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arXiv2023

On the structure of the $RO(G)$-graded homotopy of $H\underline{M}$ for cyclic $p$-groups

We study the structure of the $RO(G)$-graded homotopy Mackey functors of any Eilenberg-MacLane spectrum $H\underline{M}$ for $G$ a cyclic $p$-group. When $\underline{R}$ is a Green functor, we define orientation classes $u_V$ for $H\underline{R}$ and deduce a generalized gold relation. We deduce the $a_V,u_V$-isomorphism regions of the $RO(G)$-graded homotopy Mackey functors and prove two induction theorems. As applications, we compute the positive cone of $H\underline{\mathbb{A}}$, as well as the positive and negative cones of $H\underline{\mathbb{Z}}$. The latter two cones are essential to the slice spectral sequences of $MU^{((C_{2^n}))}$ and its variants.

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