- PII
- S3034504925010096-1
- DOI
- 10.7868/S3034504925010096
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume 521 / Issue number 1
- Pages
- 72-80
- Abstract
- The note provides a new formula for the companion matrix of the superposition of two polynomials over a commutative ring. The results obtained are used to provide a constructive proof of Plans’ theorem for two-bridge knots, which states that the first homology group of an odd-sheeted cyclic covering of a three-dimensional sphere branched over a given knot is the direct sum of two copies of some Abelian group. A similar result is also true for the homology of even-sheeted coverings factored by the reduced homology group of a two-sheeted covering. The structure of the above mentioned Abelian groups is described through Chebyshev polynomials of the second and fourth kind.
- Keywords
- нормальная форма Смита сопровождающая матрица узел группа гомологий разветленное накрытие
- Date of publication
- 03.02.2025
- Year of publication
- 2025
- Number of purchasers
- 0
- Views
- 68
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