27,148 research outputs found
Classification of Links Up to 0-Solvability
The -solvable filtration of the -component smooth (string) link
concordance group, as defined by Cochran, Orr, and
Teichner, is a tool for studying smooth knot and link concordance that yields
important results in low-dimensional topology. The focus of this paper is to
give a characterization of the set of 0-solvable links. We introduce a new
equivalence relation on links called 0-solve equivalence and establish both an
algebraic and a geometric classification of , the set of links
up to 0-solve equivalence. We show that has a group structure
isomorphic to the quotient of concordance
classes of string links and classify this group, showing that Finally, using
results of Conant, Schneiderman, and Teichner, we show that 0-solvable links
are precisely the links that bound class 2 gropes and support order 2 Whitney
towers in the 4-ball.Comment: 34 page
Adic reduction to the diagonal and a relation between cofiniteness and derived completion
We prove two results about the derived functor of -adic completion: (1)
Let be a commutative noetherian ring, let be a flat noetherian
-algebra which is -adically complete with respect to some ideal
, such that is essentially of finite type over , and let
be finitely generated -modules. Then adic reduction to the diagonal
holds: . A similar result is given in the case where are
not necessarily finitely generated. (2) Let be a commutative ring, let
be a weakly proregular ideal, let be an -module, and
assume that the -adic completion of is noetherian (if is noetherian,
all these conditions are always satisfied). Then \mbox{Ext}^i_A(A/a,M) is
finitely generated for all if and only if the derived -adic
completion \L\hat{\Lambda}_{a}(M) has finitely generated cohomologies over
. The first result is a far reaching generalization of a result of
Serre, who proved this in case is a field or a discrete valuation ring and
.Comment: 12 pages. Final version, to appear in Proceedings of the AM
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