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• W1635754585 abstract "Publisher Summary This chapter provides an overview of the concordance group of knots in three-dimensional space. It begins with a review of the definitions of knots and concordance and then presents aspects of the algebraic theory of concordance. There are two related theories of concordance, one in the smooth category and the other topological. There are alternative approaches to algebraic obstructions to a knot being slice. A surgery obstruction to finding such a manifold W is determined by the Seifert form, and for a knot of Alexander polynomial one that is the only obstruction, and it vanishes. Although these powerful techniques have revealed a far greater complexity to the concordance group than had been expected, as of now they seem incapable of addressing some of the basic questions: for instance, the slice implies ribbon conjecture and problems related to torsion in the concordance group. Recent work of Cochran, Orr and Teichner has demonstrated a deep structure to the topological concordance group. A discussion of the interplay between three-dimensional knot properties and concordance is also presented in the chapter. The chapter concludes with a brief list of open problems." @default.
• W1635754585 created "2016-06-24" @default.
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• W1635754585 date "2005-01-01" @default.
• W1635754585 modified "2023-09-26" @default.
• W1635754585 title "A Survey of Classical Knot Concordance" @default.
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• W1635754585 doi "https://doi.org/10.1016/b978-044451452-3/50008-3" @default.
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