Cobordism of algebraic knots defined by Brieskorn polynomials, II
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914028252561408 |
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| author | Blanloeil, Vincent Saeki, Osamu |
| author_facet | Blanloeil, Vincent Saeki, Osamu |
| contents | In our previous paper, we obtained several results concerning cobordisms of algebraic knots associated with Brieskorn polynomials: for example, under certain conditions, we showed that the exponents are cobordism invariants. In this paper, we further obtain new results concerning the Fox--Milnor type relations, decomposition of the algebraic cobordism class of an algebraic knot associated with a Brieskorn polynomial that has a null-cobordant factor over the field of rational numbers, and cyclic suspensions of knots. As a corollary, we show that a spherical algebraic knot associated with a Brieskorn polynomial has infinite order in the knot cobordism group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03662 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cobordism of algebraic knots defined by Brieskorn polynomials, II Blanloeil, Vincent Saeki, Osamu Geometric Topology 57K45, 32S55, 57K10 In our previous paper, we obtained several results concerning cobordisms of algebraic knots associated with Brieskorn polynomials: for example, under certain conditions, we showed that the exponents are cobordism invariants. In this paper, we further obtain new results concerning the Fox--Milnor type relations, decomposition of the algebraic cobordism class of an algebraic knot associated with a Brieskorn polynomial that has a null-cobordant factor over the field of rational numbers, and cyclic suspensions of knots. As a corollary, we show that a spherical algebraic knot associated with a Brieskorn polynomial has infinite order in the knot cobordism group. |
| title | Cobordism of algebraic knots defined by Brieskorn polynomials, II |
| topic | Geometric Topology 57K45, 32S55, 57K10 |
| url | https://arxiv.org/abs/2411.03662 |