It is known that the Alexander polynomial of the sum of two knots $K=K_1\#K_2$ is equal to the product of the Alexander polynomial of the two summands $K_1$ and $K_2$. If the same true for the Alexander-Conway polynomial (AC(trefoil) $= 1 + z^2$) ?
2026-03-26 08:23:10.1774513390
Alexander-Conway polynomial of the sum of two knots
351 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in KNOT-THEORY
- Is unknot a composite knot?
- Can we modify one component of a link and keep the others unchanged
- Can we split a splittable link by applying Reidemeister moves to non-self crossings only
- Involution of the 3 and 4-holed torus and its effects on some knots and links
- Equivalence polygonal knots with smooth knots
- Can a knot diagram be recovered from this data?
- Does Seifert's algorithm produce Seifert surfaces with minimal genus?
- Equivalence of links in $R^3$ or $S^3$
- Homotopy type of knot complements
- The complement of a knot is aspherical
Related Questions in KNOT-INVARIANTS
- Can we modify one component of a link and keep the others unchanged
- Can we split a splittable link by applying Reidemeister moves to non-self crossings only
- Does Seifert's algorithm produce Seifert surfaces with minimal genus?
- Coloring of a knot diagram by a trivial quandle
- How to obtain all possible colorings of a knot diagram by a given quandle
- Are any knot volumes known to be (ir)rational? If not, then why is the question difficult?
- Alternating and Non-Altenating Knot projections with same crossing number?
- what is a delta move on a trefoil knot
- Quantum invariants of 2-knots
- On Alexander polynomial of a knot
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Yes, it is true for the Alexander-Conway polynomial.
If you still have doubts, think that both the polynomials are special cases of the HOMFLY-PT polynomial.