Zhouli Xu

activity

20142025

most citedIntersection Forms of Spin 4-Manifolds and the Pin(2)-Equivariant Mahowald Invariant

33 citations · 120 across the 19 of their papers we have counts for

collaborators

19 papers

math.AT2025

Periodicity and finite complexity in higher real $K$ -theories

Zhipeng Duan, Michael A. Hill, Guchuan Li +4

In this paper, we establish periodicity results for higher real $K$ -theories at all heights and for all finite subgroups of the Morava stabilizer group at the prime 2. We further a…

math.AT2024

On the Last Kervaire Invariant Problem

Weinan Lin, Guozhen Wang, Zhouli Xu

We prove that the element $h_{6}^{2}$ is a permanent cycle in the Adams spectral sequence. As a result, we establish the existence of smooth framed manifolds with Kervaire invariant on…

math.AT2024★ 1 cited

Machine Proofs for Adams Differentials and Extension Problems among CW Spectra

Weinan Lin, Guozhen Wang, Zhouli Xu

In this document, we describe the process of obtaining numerous Adams differentials and extensions using computational methods, as well as how to interpret the dataset uploaded to…

math.AT2023

The Adams differentials on the classes $h_{j}^{3}$

Robert Burklund, Zhouli Xu

In filtration 1 of the Adams spectral sequence, using secondary cohomology operations, Adams computed the differentials on the classes $h_{j}$ , resolving the Hopf invariant one probl…

math.AT2022★ 1 cited

The reduced ring of the $R O (C_{2})$ -graded $C_{2}$ -equivariant stable stems

Eva Belmont, Zhouli Xu, Shangjie Zhang

We describe in terms of generators and relations the ring structure of the $R O (C_{2})$ -graded $C_{2}$ -equivariant stable stems $π_{⋆}^{C_{2}}$ modulo the ideal of all nilpotent element…

math.AT2021★ 3 cited

The topological modular forms of $R P^{2}$ and $R P^{2} \land C P^{2}$

Agnès Beaudry, Irina Bobkova, Viet-Cuong Pham +1

In this paper, we study the elliptic spectral sequence computing $t m f_{*} (R P^{2})$ and $t m f_{*} (R P^{2} \land C P^{2})$ . Specifically, we compute all differenti…

math.KT2020

The Chow $t$ -structure on the $\infty$ -category of motivic spectra

Tom Bachmann, Hana Jia Kong, Guozhen Wang +1

We define the Chow $t$ -structure on the $\infty$ -category of motivic spectra $S H (k)$ over an arbitrary base field $k$ . We identify the heart of this $t$ -structure $SH(k)^{c\heartsu…

math.AT2020★ 26 cited

Stable homotopy groups of spheres

Daniel C. Isaksen, Guozhen Wang, Zhouli Xu

We discuss the current state of knowledge of stable homotopy groups of spheres. We describe a new computational method that yields a streamlined computation of the first 61 stable…

math.AT2020★ 8 cited

Stable homotopy groups of spheres: From dimension 0 to 90

Daniel C. Isaksen, Guozhen Wang, Zhouli Xu

Using techniques in motivic homotopy theory, especially the theorem of Gheorghe, the second and the third author on the isomorphism between motivic Adams spectral sequence for $C τ$ …

math.AT2019★ 10 cited

The telescope conjecture at height 2 and the tmf resolution

Agnes Beaudry, Mark Behrens, Prasit Bhattacharya +2

Mahowald proved the height 1 telescope conjecture at the prime 2 as an application of his seminal work on bo-resolutions. In this paper we study the height 2 telescope conjecture a…

math.AT2019★ 33 cited

Intersection Forms of Spin 4-Manifolds and the Pin(2)-Equivariant Mahowald Invariant

Michael J. Hopkins, Jianfeng Lin, XiaoLin Danny Shi +1

In studying the "11/8-Conjecture" on the Geography Problem in 4-dimensional topology, Furuta proposed a question on the existence of Pin(2)-equivariant stable maps between certain…

math.AT2018★ 10 cited

The slice spectral sequence of a $C_{4}$ -equivariant height-4 Lubin-Tate theory

Michael A. Hill, XiaoLin Danny Shi, Guozhen Wang +1

We completely compute the slice spectral sequence of the $C_{4}$ -spectrum $B P^{((C_{4}))} ⟨ 2 ⟩$ . After periodization and $K (4)$ -localization, this spectrum is equivalent to…

math.AT2018★ 7 cited

The special fiber of the motivic deformation of the stable homotopy category is algebraic

Bogdan Gheorghe, Guozhen Wang, Zhouli Xu

For each prime $p$ , we define a $t$ -structure on the category $S^{0, 0} / τ - Mod_{ha r m}^{b}$ of harmonic $C$ -motivic left module spectra over $\widehat…

math.AT2017★ 2 cited

Hurewicz Images of Real Bordism Theory and Real Johnson-Wilson Theories

Guchuan Li, XiaoLin Danny Shi, Guozhen Wang +1

We show that the Hopf elements, the Kervaire classes, and the $κ ˉ$ -family in the stable homotopy groups of spheres are detected by the Hurewicz map from the sphere spectrum to t…

math.AT2017★ 7 cited

Some extensions in the Adams spectral sequence and the 51-stem

Guozhen Wang, Zhouli Xu

We show a few nontrivial extensions in the classical Adams spectral sequence. In particular, we compute that the 2-primary part of $π_{51}$ is $\mathbb{Z}/8\oplus\mathbb{Z}/8\oplus…

math.AT2016★ 2 cited

The algebraic Atiyah-Hirzebruch spectral sequence of real projective spectra

Guozhen Wang, Zhouli Xu

In this note, we use Curtis's algorithm and the Lambda algebra to compute the algebraic Atiyah-Hirzebruch spectral sequence of the suspension spectrum of $R P^{\infty}$ with…

math.AT2016★ 1 cited

The triviality of the 61-stem in the stable homotopy groups of spheres

Guozhen Wang, Zhouli Xu

We prove that the 2-primary $π_{61}$ is zero. As a consequence, the Kervaire invariant element $θ_{5}$ is contained in the strictly defined 4-fold Toda bracket $\langle 2, θ_4, θ_4,…

math.AT2014★ 1 cited

Motivic Stable Homotopy and the Stable 51 and 52 Stems

Daniel C. Isaksen, Zhouli Xu

We establish a differential $d_{2} (D_{1}) = h_{0}^{2} h_{3} g_{2}$ in the $51$ -stem of the Adams spectral sequence at the prime $2$ , which gives the first correct calculation of the stable 51 and…

math.AT2014★ 8 cited

The strong Kervaire invariant problem in dimension 62

Zhouli Xu

Using a Toda bracket computation $⟨ θ_{4}, 2, σ^{2} ⟩$ due to Daniel C. Isaksen [11], we investigate the $45$ -stem more thoroughly. We prove that $θ_{4}^{2} = 0$ using a $4$ -fold…

Periodicity and finite complexity in higher real K-theories

On the Last Kervaire Invariant Problem

Machine Proofs for Adams Differentials and Extension Problems among CW Spectra

The Adams differentials on the classes hj3​

The reduced ring of the RO(C2​)-graded C2​-equivariant stable stems

The topological modular forms of RP2 and RP2∧CP2

The Chow t-structure on the ∞-category of motivic spectra

Stable homotopy groups of spheres

Stable homotopy groups of spheres: From dimension 0 to 90

The telescope conjecture at height 2 and the tmf resolution

Intersection Forms of Spin 4-Manifolds and the Pin(2)-Equivariant Mahowald Invariant

The slice spectral sequence of a C4​-equivariant height-4 Lubin-Tate theory

The special fiber of the motivic deformation of the stable homotopy category is algebraic

Hurewicz Images of Real Bordism Theory and Real Johnson-Wilson Theories

Some extensions in the Adams spectral sequence and the 51-stem

The algebraic Atiyah-Hirzebruch spectral sequence of real projective spectra

The triviality of the 61-stem in the stable homotopy groups of spheres

Motivic Stable Homotopy and the Stable 51 and 52 Stems

The strong Kervaire invariant problem in dimension 62

Periodicity and finite complexity in higher real $K$ -theories

The Adams differentials on the classes $h_{j}^{3}$

The reduced ring of the $R O (C_{2})$ -graded $C_{2}$ -equivariant stable stems

The topological modular forms of $R P^{2}$ and $R P^{2} \land C P^{2}$

The Chow $t$ -structure on the $\infty$ -category of motivic spectra

The slice spectral sequence of a $C_{4}$ -equivariant height-4 Lubin-Tate theory