Doomsday conjecture

In algebraic topology, the doomsday conjecture was a conjecture about Ext groups over the Steenrod algebra made by Joel Cohen, named by Michael Barratt, published by Template:Harvtxt and disproved by Template:Harvtxt. Template:Harvtxt stated a modified version called the new doomsday conjecture.

The original doomsday conjecture was that for any prime p and positive integer s there are only a finite number of permanent cycles in

${\text{Ext}}_{A_{*}}^{s,*}(Z/pZ,Z/pZ).$

Template:Harvtxt found an infinite number of permanent cycles for p = s = 2, disproving the conjecture. Minami's new doomsday conjecture is a weaker form stating (in the case p = 2) that there are no nontrivial permanent cycles in the image of (Sq⁰)ⁿ for n sufficiently large depending on s.

References

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