33 citations · 120 across the 19 of their papers we have counts for
18 papers · 1 filter
Periodicity and finite complexity in higher real -theories
Zhipeng Duan, Michael A. Hill, Guchuan Li +4
In this paper, we establish periodicity results for higher real -theories at all heights and for all finite subgroups of the Morava stabilizer group at the prime 2. We further a…
On the Last Kervaire Invariant Problem
Weinan Lin, Guozhen Wang, Zhouli Xu
We prove that the element is a permanent cycle in the Adams spectral sequence. As a result, we establish the existence of smooth framed manifolds with Kervaire invariant on…
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…
The Adams differentials on the classes
Robert Burklund, Zhouli Xu
In filtration 1 of the Adams spectral sequence, using secondary cohomology operations, Adams computed the differentials on the classes , resolving the Hopf invariant one probl…
The reduced ring of the -graded -equivariant stable stems
Eva Belmont, Zhouli Xu, Shangjie Zhang
We describe in terms of generators and relations the ring structure of the -graded -equivariant stable stems modulo the ideal of all nilpotent element…
The topological modular forms of and
Agnès Beaudry, Irina Bobkova, Viet-Cuong Pham +1
In this paper, we study the elliptic spectral sequence computing and . Specifically, we compute all differenti…
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…
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 …
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…
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…
The slice spectral sequence of a -equivariant height-4 Lubin-Tate theory
Michael A. Hill, XiaoLin Danny Shi, Guozhen Wang +1
We completely compute the slice spectral sequence of the -spectrum . After periodization and -localization, this spectrum is equivalent to…
The special fiber of the motivic deformation of the stable homotopy category is algebraic
Bogdan Gheorghe, Guozhen Wang, Zhouli Xu
For each prime , we define a -structure on the category of harmonic -motivic left module spectra over $\widehat…
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 -family in the stable homotopy groups of spheres are detected by the Hurewicz map from the sphere spectrum to t…
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 is $\mathbb{Z}/8\oplus\mathbb{Z}/8\oplus…
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 with…
The triviality of the 61-stem in the stable homotopy groups of spheres
Guozhen Wang, Zhouli Xu
We prove that the 2-primary is zero. As a consequence, the Kervaire invariant element is contained in the strictly defined 4-fold Toda bracket $\langle 2, θ_4, θ_4,…
Motivic Stable Homotopy and the Stable 51 and 52 Stems
Daniel C. Isaksen, Zhouli Xu
We establish a differential in the -stem of the Adams spectral sequence at the prime , which gives the first correct calculation of the stable 51 and…
The strong Kervaire invariant problem in dimension 62
Zhouli Xu
Using a Toda bracket computation due to Daniel C. Isaksen [11], we investigate the -stem more thoroughly. We prove that using a -fold…