scholarly journals Isotropic stable motivic homotopy groups of spheres

2021 ◽  
Vol 383 ◽  
pp. 107696
Author(s):  
Fabio Tanania
Keyword(s):  
Homotopy Groups ◽  
Homotopy Groups Of Spheres ◽  
Motivic Homotopy

scholarly journals Stable homotopy groups of spheres

2020 ◽  
Vol 117 (40) ◽  
pp. 24757-24763
Author(s):  
Daniel C. Isaksen ◽  
Guozhen Wang ◽  
Zhouli Xu
Keyword(s):  
Homotopy Theory ◽  
Computational Method ◽  
Stable Homotopy ◽  
Homotopy Groups ◽  
Mathematical Tool ◽  
Homotopy Groups Of Spheres ◽  
Stable Homotopy Groups ◽  
Current State ◽  
Motivic Homotopy Theory ◽  
Motivic Homotopy

We discuss the current state of knowledge of stable homotopy groups of spheres. We describe a computational method using motivic homotopy theory, viewed as a deformation of classical homotopy theory. This yields a streamlined computation of the first 61 stable homotopy groups and gives information about the stable homotopy groups in dimensions 62 through 90. As an application, we determine the groups of homotopy spheres that classify smooth structures on spheres through dimension 90, except for dimension 4. The method relies more heavily on machine computations than previous methods and is therefore less prone to error. The main mathematical tool is the Adams spectral sequence.

scholarly journals The structure of motivic homotopy groups

2016 ◽  
Vol 23 (1) ◽  
pp. 389-397 ◽  
Author(s):  
Bogdan Gheorghe ◽  
Daniel C. Isaksen
Keyword(s):  
Homotopy Groups ◽  
Motivic Homotopy

scholarly journals A Conjecture on Homotopy Groups of Spheres, Details on the Algebra of Higher Cohomology Operations

2009 ◽  
Vol 16 (1) ◽  
pp. 1-12
Author(s):  
Hans-Joachim Baues
Keyword(s):  
Homotopy Groups ◽  
Homotopy Groups Of Spheres ◽  
Cohomology Operations

Abstract The computation of the algebra of secondary cohomology operations in [Baues, The algebra of secondary cohomology operations, Birkhäuser Verlag, 2006] leads to a conjecture concerning the algebra of higher cohomology operations in general and an Ext-formula for the homotopy groups of spheres. This conjecture is discussed in detail in this paper.

Some infinite families in the stable homotopy of spheres

1987 ◽  
Vol 101 (3) ◽  
pp. 477-485 ◽  
Author(s):  
Wen-Hsiung Lin
Keyword(s):  
Spectral Sequence ◽  
Adams Spectral Sequence ◽  
Stable Homotopy ◽  
Homotopy Groups ◽  
Homotopy Groups Of Spheres ◽  
Stable Homotopy Groups ◽  
Stable Homotopy Of Spheres

The classical Adams spectral sequence [1] has been an important tool in the computation of the stable homotopy groups of spheres . In this paper we make another contribution to this computation.

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

2017 ◽  
Vol 186 (2) ◽  
pp. 501-580 ◽  
Author(s):  
Guozhen Wang ◽  
Zhouli Xu
Keyword(s):  
Stable Homotopy ◽  
Homotopy Groups ◽  
Homotopy Groups Of Spheres ◽  
Stable Homotopy Groups

scholarly journals Non-triviality of an element in the stable homotopy groups of spheres

1975 ◽  
Vol 5 (1) ◽  
pp. 115-125 ◽  
Author(s):  
Shichirô Oka ◽  
Hirosi Toda
Keyword(s):  
Stable Homotopy ◽  
Homotopy Groups ◽  
Homotopy Groups Of Spheres ◽  
Stable Homotopy Groups

The Double Suspension and Exponents of the Homotopy Groups of Spheres

1979 ◽  
Vol 110 (3) ◽  
pp. 549 ◽  
Author(s):  
F. R. Cohen ◽  
J. C. Moore ◽  
J. A. Neisendorfer
Keyword(s):  
Homotopy Groups ◽  
Homotopy Groups Of Spheres
Sign in / Sign up

Export Citation Format

Share Document