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pro vyhledávání: '"Mahowald, A"'
We introduce the $C_{p^n}$-Mahowald invariant: a relation $\pi_\star S_{C_{p^{n-1}}} \rightharpoonup \pi_\ast S$ between the equivariant and classical stable stems which reduces to the classical Mahowald invariant when $n=1$. We compute the $C_{p^n}$
Externí odkaz:
http://arxiv.org/abs/2411.00421
Autor:
Botvinnik, Boris, Quigley, J. D.
We deduce the existence of smooth $U(1)$- and $Sp(1)$-actions on certain exotic spheres using complex and quaternionic analogues of the Mahowald {(root)} invariant. In particular, we prove that the complex (respectively, quaternionic) Mahowald invari
Externí odkaz:
http://arxiv.org/abs/2309.04275
Autor:
Quigley, J. D.
Publikováno v:
Algebr. Geom. Topol. 22 (2022) 1789-1839
The $2$-primary homotopy $\beta$-family, defined as the collection of Mahowald invariants of Mahowald invariants of $2^i$, $i \geq 1$, is an infinite collection of periodic elements in the stable homotopy groups of spheres. In this paper, we calculat
Externí odkaz:
http://arxiv.org/abs/1911.07975
Autor:
Quigley, J. D.
The motivic Mahowald invariant was introduced in \cite{Qui19a} and \cite{Qui19b} to study periodicity in the $\mathbb{C}$- and $\mathbb{R}$-motivic stable stems. In this paper, we define the motivic Mahowald invariant over any field $F$ of characteri
Externí odkaz:
http://arxiv.org/abs/1905.03902
Autor:
Quigley, J. D.
We generalize the Mahowald invariant to the $\mathbb{R}$-motivic and $C_2$-equivariant settings. For all $i>0$ with $i \equiv 2,3 \mod 4$, we show that the $\mathbb{R}$-motivic Mahowald invariant of $(2+\rho \eta)^i \in \pi_{0,0}^{\mathbb{R}}(S^{0,0}
Externí odkaz:
http://arxiv.org/abs/1904.12996
Autor:
Isaksen, Daniel C.
We study the Mahowald operator $M = \langle g_2,h_0^3, - \rangle$ in the cohomology of the Steenrod algebra. We show that the operator interacts well with the cohomology of $A(2)$, in both the classical and $\mathbb{C}$-motivic contexts. This general
Externí odkaz:
http://arxiv.org/abs/2001.01758
Autor:
SHICK, PAUL1 shick@jcu.edu
Publikováno v:
Homology, Homotopy & Applications. 2020, Vol. 22 Issue 2, p59-72. 14p.
Autor:
Shick, Paul
Mahowald's conjecture arose as part of a program attempting to view chromatic phenomena in stable homotopy theory through the lens of the classical Adams spectral sequence. The conjecture predicts the existence of nonzero classes in the cohomology of
Externí odkaz:
http://arxiv.org/abs/1905.02625
Autor:
Mead, Carver1 (AUTHOR) carver@caltech.edu
Publikováno v:
Neural Computation. Mar2023, Vol. 35 Issue 3, p343-383. 41p. 1 Illustration, 4 Diagrams, 4 Graphs.
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 representation spheres. In this paper, we present a complete solution
Externí odkaz:
http://arxiv.org/abs/1812.04052