Geodesic
ℤ∕p × ℤ∕p actions on Sn × Sn
Fowler, Jim1 ; Thatcher, Courtney2
1 Department of Mathematics, The Ohio State University, Columbus, OH, United States
2 Department of Mathematics and Computer Science, University of Puget Sound, Tacoma, WA, United States
Algebraic and Geometric Topology, Tome 24 (2024) no. 4, pp. 1841-1862

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We determine the homotopy type of quotients of Sn × Sn by free actions of ℤ∕p × ℤ∕p where 2p > n + 3. Much like free ℤ∕p actions, they can be classified via the first p–localized k–invariant, but there are restrictions on the possibilities, and these restrictions are sufficient to determine every possibility in the n = 3 case. We use this to complete the classification of free ℤ∕p × ℤ∕p actions on S3 × S3 for p > 3 by reducing the problem to the simultaneous classification of pairs of binary quadratic forms. Although the restrictions are not sufficient to determine which k–invariants are realizable in general, they can sometimes be used to rule out free actions by groups that contain ℤ∕p × ℤ∕p as a normal abelian subgroup.

DOI : 10.2140/agt.2024.24.1841
Keywords: group actions on manifolds, Postnikov towers, binary quadratic forms

Fowler, Jim 1 ; Thatcher, Courtney 2

1 Department of Mathematics, The Ohio State University, Columbus, OH, United States
2 Department of Mathematics and Computer Science, University of Puget Sound, Tacoma, WA, United States 
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Fowler, Jim; Thatcher, Courtney. ℤ∕p × ℤ∕p actions on Sn × Sn. Algebraic and Geometric Topology, Tome 24 (2024) no. 4, pp. 1841-1862. doi: 10.2140/agt.2024.24.1841

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