-cobordism for links in
Author:
Tim D. Cochran
Journal:
Trans. Amer. Math. Soc. 327 (1991), 641-654
MSC:
Primary 57M25
DOI:
https://doi.org/10.1090/S0002-9947-1991-1055569-2
MathSciNet review:
1055569
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Abstract | References | Similar Articles | Additional Information
Abstract: We give an explicit finite set of (based) links which generates, under connected sum, the -cobordism classes of links. We show that the union of these generating sets,
, is not a generating set for
-cobordism classes or even
-cobordism classes.
For -component links in
we define
-corbordism and show that the concordance invariants
, previously defined by the author, are invariants under
-cobordism. Moreover we show that the
-cobordism classes of links (with linking number 0) is a free abelian group of rank
, detected precisely by
. We write down a basis. The union of these bases
is not a generating set for
or
-cobordism classes. However, we can show that
is an isomorphism from the group of
-cobordism classes to the subgroup
of linearly recurrent sequences, so a basis exists by work of T. Jin.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1991-1055569-2
Keywords:
Link,
concordance,
cobordism,
-invariants,
Massey products
Article copyright:
© Copyright 1991
American Mathematical Society