Zobrazeno 1 - 10
of 261
pro vyhledávání: '"55Q45"'
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 one in dimension 126, thereby resolving the final case of the Kervaire i
Externí odkaz:
http://arxiv.org/abs/2412.10879
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 Zenodo. Detailed proofs of the machine-generated results are also prov
Externí odkaz:
http://arxiv.org/abs/2412.10876
Autor:
Kang, Mohammad Behzad, Salch, Andrew
We calculate the cohomology of the extended Morava stabilizer group of height $n$, with trivial mod $p$ coefficients, for all heights $n$ and all primes $p>>n$. The result is an exterior algebra on $n$ generators. A brief sketch of the method: we int
Externí odkaz:
http://arxiv.org/abs/2410.24171
Autor:
Bobkova, Irina, Quigley, J. D.
We produce a new $192$-periodic infinite family of simple $\eta$-torsion elements in the stable homotopy groups of spheres using the $\mathit{tmf}$-Hurewicz homomorphism and the complex projective plane.
Comment: 4 pages. Comments welcome!
Comment: 4 pages. Comments welcome!
Externí odkaz:
http://arxiv.org/abs/2410.21181
We study the $\mathbb{F}_2$-synthetic Adams spectral sequence. We obtain new computational information about $\mathbb{C}$-motivic and classical stable homotopy groups.
Externí odkaz:
http://arxiv.org/abs/2408.00987
Autor:
Minami, Haruo
Let $G$ be a compact simple Lie group equipped with the left invariant framing $L$. It is known that there are several groups $G$ such that $(G, L)$ is non-null framed bordant. Previously we gave an alternative proof of these results using the decomp
Externí odkaz:
http://arxiv.org/abs/2408.02682
Autor:
Minami, Haruo
Let $[SU(2n),\mathscr{L}]$ denote the bordism class of $SU(2n)$ $(n\ge 2)$ equipped with the left invariant framing $\mathscr{L}$. Then it is well known that $e_\mathbb{C}([SU(2n), \mathscr{L}])=0$ in $\mathbb{O}/\mathbb{Z}$ where $e_\mathbb{C}$ deno
Externí odkaz:
http://arxiv.org/abs/2406.11878
We compute the 2-primary $C_2$-equivariant stable homotopy groups $\pi^{C_2}_{s,c}$ for stems between 0 and 25 (i.e., $0 \leq s \leq 25$) and for coweights between -1 and 7 (i.e., $-1 \leq c \leq 7)$. Our results, combined with periodicity isomorphis
Externí odkaz:
http://arxiv.org/abs/2404.14627
We identify seven new $192$-periodic infinite families of elements in the $2$-primary stable homotopy groups of spheres. Although their Hurewicz image is trivial for topological modular forms, they remain nontrivial after $\mathrm{T}(2)$- as well as
Externí odkaz:
http://arxiv.org/abs/2404.10062
This paper explores various differentiable structures on the product manifold $M \times \mathbb{S}^k$, where $M$ is either a 4-dimensional closed oriented manifold or a simply connected 5-dimensional closed manifold. We identify the possible stable h
Externí odkaz:
http://arxiv.org/abs/2402.18914