# SATELLITES AND CONCORDANCE OF KNOTS IN 3 MANIFOLDS

Friedl, S
Nagel, M
Orson, P
Powell, M

15 February 2019

## Journal:

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY

## Last Updated:

2019-04-26T15:14:59.357+01:00

4

371

## DOI:

10.1090/tran/7313

2279-2306

## abstract:

Given a 3-manifold $Y$ and a free homotopy class in $[S^1,Y]$, we investigate
the set of topological concordance classes of knots in $Y \times [0,1]$
representing the given homotopy class. The concordance group of knots in the
3-sphere acts on this set. We show in many cases that the action is not
transitive, using two techniques. Our first technique uses Reidemeister torsion
invariants, and the second uses linking numbers in covering spaces. In
particular, we show using covering links that for the trivial homotopy class,
and for any 3-manifold that is not the 3-sphere, the set of orbits is infinite.
On the other hand, for the case that $Y=S^1 \times S^2$, we apply topological
surgery theory to show that all knots with winding number one are concordant.

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