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Knot Floer homology of satellite knots with (1, 1) patterns.
- Source :
- Selecta Mathematica, New Series; Sep2023, Vol. 29 Issue 4, p1-63, 63p
- Publication Year :
- 2023
-
Abstract
- For pattern knots admitting genus-one doubly pointed bordered Heegaard diagrams, we give an immersed-curve approach to compute the knot Floer chain complexes of the corresponding satellite knots. In particular, this approach provides a convenient way to compute the knot concordance invariant τ . For patterns P obtained from two-bridge links b(p, q), we derive a formula for the τ -invariant of P (T 2 , 3) and P (- T 2 , 3) in terms of (p, q). We use this formula to study whether such patterns induce homomorphisms on the knot concordance group, providing a glimpse at a conjecture due to Hedden. [ABSTRACT FROM AUTHOR]
- Subjects :
- FLOER homology
HOMOMORPHISMS
KNOT theory
BRIDGES
Subjects
Details
- Language :
- English
- ISSN :
- 10221824
- Volume :
- 29
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- Selecta Mathematica, New Series
- Publication Type :
- Academic Journal
- Accession number :
- 169912253
- Full Text :
- https://doi.org/10.1007/s00029-023-00859-6