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# Homotopy of Knots and the Alexander Polynomial

Published:1999-09-01
Printed: Sep 1999
• David Austin
• Dale Rolfsen
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## Abstract

Any knot in a 3-dimensional homology sphere is homotopic to a knot with trivial Alexander polynomial.
 MSC Classifications: 57N10 - Topology of general $3$-manifolds [See also 57Mxx] 57M05 - Fundamental group, presentations, free differential calculus 57M25 - Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57N65 - Algebraic topology of manifolds

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