A Fox–Milnor theorem for the Alexander polynomial of knotted 2-spheres in $S^4$

Moussard, Delphine; Wagner, Emmanuel

doi:10.2969/jmsj/82218221

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Alexander Invariants1

Seifert Matrices1

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2022

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“…Nakanishi and Nishizawa gave a topological condition on a 2-knot ensuring that its Alexander polynomial is symmetric [102]. Moussard and Wagner provide conditions for the Alexander polynomial of certain ribbon 2-knots to factor as f (t)f (t −1 ) [99].…”

Section: Alexander Invariantsmentioning

confidence: 99%

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Invariants of $2$-knots

Conway¹

2022

Preprint

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This short survey, which was written to accompany a minicourse at the BIRS conference 'Topology in dimension 4.5', concerns invariants of knotted 2-spheres in S 4 , also known as 2-knots. It covers invariants extracted from the algebraic topology of the knot exterior, including Alexander invariants, the Farber-Levine pairing and Casson-Gordon invariants, as well as gauge theoretic and combinatorial invariants. Details are scarce and new results inexistant.

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Section: Alexander Invariantsmentioning

confidence: 99%

“…; see e.g. [42,99]. In particular, in this case, the Alexander module admits a square presentation matrix.…”

Section: Seifert Matricesmentioning

confidence: 99%