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New
infinite families in the stable homotopy groups of
spheres
Prasit Bhattacharya, Irina Bobkova and J D Quigley |
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Geometry & Topology 30 (2026) 2367–2393
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Abstract |
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We identify seven new -periodic infinite families of elements in the -primary stable homotopy groups of spheres, all of which have trivial image under the Hurewicz map for topological modular forms. We prove that these families are nontrivial after - as well as -localization. We also obtain new information about -torsion and -divisibility of some of the previously known -periodic infinite families in the stable stems. |
Keywords
stable homotopy groups of spheres, stable homotopy theory,
v2-periodic families, topological modular forms, chromatic
homotopy theory
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Mathematical Subject Classification
Primary: 55Q10, 55Q45, 55Q51
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References |
Publication
Received: 13 January 2025
Revised: 22 January 2026
Accepted: 20 February 2026
Published: 31 July 2026
Proposed: Haynes R Miller
Seconded: Agnès Beaudry, Kirsten Wickelgren
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Authors |
| Prasit Bhattacharya | |
| New Mexico State University Las Cruces, NM United States |
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| Irina Bobkova | |
| Department of Mathematics Texas A&M University College Station, TX United States |
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| J D Quigley | |
| Department of Mathematics University of Virginia Charlottesville, VA United States |
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| © 2026 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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