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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMay 7th 2013
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded to [[homotopy groups of spheres]] the table | $k =$ | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | $\cdots$ | |--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--| | $\pi_k(\mathbb{S}) = $ | $\mathbb{Z}$ | $\mathbb{Z}_2$ | $\mathbb{Z}_2$ | $\mathbb{Z}_{24}$ | $0$ | $0$ | $\mathbb{Z}_2$ | $\mathbb{Z}_{240}$ | $(\mathbb{Z}_2)^2$ | $(\mathbb{Z}_2)^3$ | $\mathbb{Z}_6$ | $\mathbb{Z}_{504}$ | $0$ | $\mathbb{Z}_3$ | $(\mathbb{Z}_2)^2$ | $\mathbb{Z}_{480} \oplus \mathbb{Z}_2$ |

   added to homotopy groups of spheres the table

   $k =$	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	$\cdots$
   $\pi_k(\mathbb{S}) =$	$\mathbb{Z}$	$\mathbb{Z}_2$	$\mathbb{Z}_2$	$\mathbb{Z}_{24}$	$0$	$0$	$\mathbb{Z}_2$	$\mathbb{Z}_{240}$	$(\mathbb{Z}_2)^2$	$(\mathbb{Z}_2)^3$	$\mathbb{Z}_6$	$\mathbb{Z}_{504}$	$0$	$\mathbb{Z}_3$	$(\mathbb{Z}_2)^2$	$\mathbb{Z}_{480} \oplus \mathbb{Z}_2$

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeNov 18th 2013
   • (edited Feb 8th 2017)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded [p-component tables](http://ncatlab.org/nlab/show/homotopy+groups+of+spheres#Tables) stolen from Allen Hatcher's website, and added an example for how to read them

   added p-component tables stolen from Allen Hatcher’s website, and added an example for how to read them

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeDec 4th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Hirosi Toda]], _Composition Methods in Homotopy Groups of Spheres_, Annals of Mathematics Studies Vol. 49, Princeton University Press (1962) ([jstor:j.ctt1bgzb5t](https://www.jstor.org/stable/j.ctt1bgzb5t)) <a href="https://ncatlab.org/nlab/revision/diff/homotopy+groups+of+spheres/42">diff</a>, <a href="https://ncatlab.org/nlab/revision/homotopy+groups+of+spheres/42">v42</a>, <a href="https://ncatlab.org/nlab/show/homotopy+groups+of+spheres">current</a>

   added pointer to:

   • Hirosi Toda, Composition Methods in Homotopy Groups of Spheres, Annals of Mathematics Studies Vol. 49, Princeton University Press (1962) (jstor:j.ctt1bgzb5t)

   diff, v42, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeFeb 4th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to the recent * [[Daniel Isaksen]], [[Guozhen Wang]], [[Zhouli Xu]], _Stable homotopy groups of spheres_ ([arXiv:2001.04247](https://arxiv.org/abs/2001.04247)) <a href="https://ncatlab.org/nlab/revision/diff/homotopy+groups+of+spheres/47">diff</a>, <a href="https://ncatlab.org/nlab/revision/homotopy+groups+of+spheres/47">v47</a>, <a href="https://ncatlab.org/nlab/show/homotopy+groups+of+spheres">current</a>

   added pointer to the recent

   • Daniel Isaksen, Guozhen Wang, Zhouli Xu, Stable homotopy groups of spheres (arXiv:2001.04247)

   diff, v47, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeFeb 8th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added publication data for: * [[Mark Mahowald]], [[Doug Ravenel]], _Towards a Global Understanding of the Homotopy Groups of Spheres_, in: [[Samuel Gitler]] (ed.): _The Lefschetz Centennial Conference: Proceedings on Algebraic Topology II_, Contemporary Mathematics volume 58, AMS 1987 ([pdf](http://www.math.rochester.edu/people/faculty/doug/mypapers/global.pdf), [[MahowaldRavenelHomotopyGroupsOfSpheres.pdf:file]], [ISBN:978-0-8218-5063-3](https://bookstore.ams.org/conm-58-2)) <a href="https://ncatlab.org/nlab/revision/diff/homotopy+groups+of+spheres/48">diff</a>, <a href="https://ncatlab.org/nlab/revision/homotopy+groups+of+spheres/48">v48</a>, <a href="https://ncatlab.org/nlab/show/homotopy+groups+of+spheres">current</a>

   I have added publication data for:

   • Mark Mahowald, Doug Ravenel, Towards a Global Understanding of the Homotopy Groups of Spheres, in: Samuel Gitler (ed.): The Lefschetz Centennial Conference: Proceedings on Algebraic Topology II, Contemporary Mathematics volume 58, AMS 1987 (pdf, MahowaldRavenelHomotopyGroupsOfSpheres.pdf:file, ISBN:978-0-8218-5063-3)

   diff, v48, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeFeb 8th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added publication data to: * [[Daniel Isaksen]], [[Guozhen Wang]], [[Zhouli Xu]], _Stable homotopy groups of spheres_, PNAS October 6, 2020 117 (40) 24757-2476 ([arXiv:2001.04247](https://arxiv.org/abs/2001.04247), [doi:10.1073/pnas.2012335117](https://doi.org/10.1073/pnas.2012335117)) <a href="https://ncatlab.org/nlab/revision/diff/homotopy+groups+of+spheres/48">diff</a>, <a href="https://ncatlab.org/nlab/revision/homotopy+groups+of+spheres/48">v48</a>, <a href="https://ncatlab.org/nlab/show/homotopy+groups+of+spheres">current</a>

   I have added publication data to:

   • Daniel Isaksen, Guozhen Wang, Zhouli Xu, Stable homotopy groups of spheres, PNAS October 6, 2020 117 (40) 24757-2476 (arXiv:2001.04247, doi:10.1073/pnas.2012335117)

   diff, v48, current

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeFeb 11th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Daniel Isaksen]], [[Guozhen Wang]], [[Zhouli Xu]], _More stable stems_ ([arXiv:2001.04511](https://arxiv.org/abs/2001.04511)) <a href="https://ncatlab.org/nlab/revision/diff/homotopy+groups+of+spheres/49">diff</a>, <a href="https://ncatlab.org/nlab/revision/homotopy+groups+of+spheres/49">v49</a>, <a href="https://ncatlab.org/nlab/show/homotopy+groups+of+spheres">current</a>

   added pointer to:

   • Daniel Isaksen, Guozhen Wang, Zhouli Xu, More stable stems (arXiv:2001.04511)

   diff, v49, current

8. • CommentRowNumber8.
   • CommentAuthornLab edit announcer
   • CommentTimeApr 3rd 2024
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexfixed Hatcher links BachoSeven <a href="https://ncatlab.org/nlab/revision/diff/homotopy+groups+of+spheres/54">diff</a>, <a href="https://ncatlab.org/nlab/revision/homotopy+groups+of+spheres/54">v54</a>, <a href="https://ncatlab.org/nlab/show/homotopy+groups+of+spheres">current</a>

   fixed Hatcher links

   BachoSeven

   diff, v54, current

9. • CommentRowNumber9.
   • CommentAuthorperezl.alonso
   • CommentTimeApr 17th 2024
   • PermaLink
   Author: perezl.alonso
   Format: MarkdownItexpointer * Prasit Bhattacharya, Irina Bobkova, J.D. Quigley. *New infinite families in the stable homotopy groups of spheres* (2024). ([arXiv:2404.10062](https://arxiv.org/abs/2404.10062)). <a href="https://ncatlab.org/nlab/revision/diff/homotopy+groups+of+spheres/56">diff</a>, <a href="https://ncatlab.org/nlab/revision/homotopy+groups+of+spheres/56">v56</a>, <a href="https://ncatlab.org/nlab/show/homotopy+groups+of+spheres">current</a>

   pointer

   • Prasit Bhattacharya, Irina Bobkova, J.D. Quigley. New infinite families in the stable homotopy groups of spheres (2024). (arXiv:2404.10062).

   diff, v56, current

10. • CommentRowNumber10.
    • CommentAuthornLab edit announcer
    • CommentTimeApr 30th 2024
    • PermaLink
    Author: nLab edit announcer
    Format: MarkdownItexWorking link for "Homotopy groups of spheres and low-dimensional topology" Natalie Stewart <a href="https://ncatlab.org/nlab/revision/diff/homotopy+groups+of+spheres/57">diff</a>, <a href="https://ncatlab.org/nlab/revision/homotopy+groups+of+spheres/57">v57</a>, <a href="https://ncatlab.org/nlab/show/homotopy+groups+of+spheres">current</a>

    Working link for “Homotopy groups of spheres and low-dimensional topology”

    Natalie Stewart

    diff, v57, current

11. • CommentRowNumber11.
    • CommentAuthornLab edit announcer
    • CommentTimeDec 6th 2024
    • PermaLink
    Author: nLab edit announcer
    Format: MarkdownItexAdded a couple of references on nontriviality of homotopy groups of 2-sphere and presentations as centers of some finitely presented groups Nikita Golub <a href="https://ncatlab.org/nlab/revision/diff/homotopy+groups+of+spheres/59">diff</a>, <a href="https://ncatlab.org/nlab/revision/homotopy+groups+of+spheres/59">v59</a>, <a href="https://ncatlab.org/nlab/show/homotopy+groups+of+spheres">current</a>

    Added a couple of references on nontriviality of homotopy groups of 2-sphere and presentations as centers of some finitely presented groups

    Nikita Golub

    diff, v59, current