The 0-concordance monoid admits an infinite linearly independent set

Autor:	Maggie Miller, Irving Dai
Rok vydání:	2023
Předmět:	Combinatorics Monoid Physics Group (mathematics) Applied Mathematics General Mathematics Cobordism Commutative monoid Linear independence Homology (mathematics) Mathematics::Geometric Topology Connected sum Spin-½
Zdroj:	Proceedings of the American Mathematical Society.
ISSN:	1088-6826 0002-9939
DOI:	10.1090/proc/15311
Popis:	Under the relation of 0 0 -concordance, the set of knotted 2-spheres in S 4 S^4 forms a commutative monoid M 0 \mathcal {M}_0 with the operation of connected sum. Sunukjian [Int. Math. Res. Not. IMRN 17 (2015), pp. 7950–7978] has recently shown that M 0 \mathcal {M}_0 contains a submonoid isomorphic to Z ≥ 0 \mathbb {Z}^{\ge 0} . In this note, we show that M 0 \mathcal {M}_0 contains a submonoid isomorphic to ( Z ≥ 0 ) ∞ (\mathbb {Z}^{\ge 0})^\infty . Our argument relates the 0 0 -concordance monoid to linear independence of certain Seifert solids in the spin rational homology cobordism group.
Databáze:	OpenAIRE
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