Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.15822

Equivariant formality for rational $\C_{p^k}$-spaces

Rekha Santhanam·Bittu Singh·Soumyadip Thandar
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this paper, we discuss equivariant formality for spaces equipped with a primary cyclic group action. We study the behavior of equivariant formality with some topological constructions. The algebraic complexity needs to deal with injectivity. In the end, we discuss equivariant intrinsic formality.

Explore related subjects

math.AT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Rekha Santhanam, Bittu Singh, Soumyadip Thandar. 2026-10-11. Equivariant formality for rational $\C_{p^k}$-spaces. https://arxiv.org/abs/2610.15822

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Higher order Massey products for algebras over algebraic operads

We introduce higher-order Massey products for algebras over algebraic operads. This extends the work of Fernando Muro on secondary ones. We study their basic properties and behavior with respect to morphisms of algebras and operads and give some connections to formality. We prove that these higher-order operations represent the differentials in a naturally associated operadic Eilenberg--Moore spectral sequence. We also study the interplay between particular choices of higher-order Massey products and quasi-isomorphic $\mathcal P_\infty$-structures on the homology of a $\mathcal P$-algebra. We focus on Koszul operads over a characteristic zero field and indicate how our results generalize to the non-Koszul case.

math.AT↗
arXiv2026

Equivariant Homotopy Interleaving and Persistent Whitehead Theorem

Let $G$ be a finite group. In this article, we develop some results of equivariant persistent homotopy theory for persistent $G$-spaces. We introduce the notions of $G$-stable and $G$-homotopy invariant distances and define the $G$-homotopy interleaving distance, an equivariant analogue $d^G_{HI}$ of the homotopy interleaving distance of Blumberg and Lesnick. We prove that this distance $d^G_{HI}$ is $G$-stable and $G$-homotopy invariant and establish its universality by showing that it dominates any such distance. We further prove a version of equivariant persistent Whitehead theorem relating interleavings of equivariant persistent homotopy groups to $G$-homotopy interleavings of persistent $G$-spaces. We also prove an equivariant persistent nerve lemma for equivariant good covers of persistent $G$-spaces. As a consequence, we obtain an equivariant weak law of large numbers for filtrations, providing a homotopy-theoretic consistency result for random filtrations equipped with finite group of symmetries.

math.AT↗
arXiv2026

Integral trace duality and the Witt filtration on Lubin--Tate space

Let $\mathcal O$ be the Lubin--Tate deformation ring of a one-dimensional commutative formal group of finite height $n\geq1$ over a perfect field $k$ of characteristic $p$. We identify Rezk's Witt filtration $\{I_d\}$ with the divisibility filtration of integral trace pairings on subgroup algebras of fixed source lifts. This gives the geometric recursion \[ I_{d+1}=pI_d+J_{d,z}\qquad(d\geq0), \] where $J_{d,z}$ defines the targets of order-$p^d$ quotient isogenies from a $W(k)$-valued lift $z$ of the closed point. The corrected ideal is independent of $z$. We also compute the cokernel of the universal source trace pairing over $\mathcal O$: it is $\bigoplus_{j=1}^d(\mathcal O/p^j)^{r_j-r_{j-1}}$, where $r_j$ counts order-$p^j$ subgroups of $(\mathbf Q_p/\mathbf Z_p)^n$. The same duality extends the generic trace along two-step isogeny flags to an integral surjection, even when the flag-forgetting map is not flat. This computes composition in the subring of weighted trace operations. Applications include sharp projector denominators and congruence fibre products for full-torsion loci.

math.AT↗