In
algebraic topology
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify ...
, the doomsday conjecture was a conjecture about
Ext group
In mathematics, the Ext functors are the derived functors of the Hom functor. Along with the Tor functor, Ext is one of the core concepts of homological algebra, in which ideas from algebraic topology are used to define invariants of algebraic st ...
s over the
Steenrod algebra made by Joel Cohen, named by Michael Barratt, published by and disproved by . 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
:
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 (Sq
0)
''n'' for ''n'' sufficiently large depending on ''s''.
References
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*{{Citation , last1=Minami , first1=Norihiko , title=The iterated transfer analogue of the new doomsday conjecture , doi=10.1090/S0002-9947-99-02037-1 , mr=1443884 , year=1999 , journal=
Transactions of the American Mathematical Society
The ''Transactions of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. It was established in 1900. As a requirement, all articles must be more than 15 p ...
, issn=0002-9947 , volume=351 , issue=6 , pages=2325–2351, doi-access=free
Algebraic topology