Back
0

Knot Theory

Description: Test your knowledge of Knot Theory, a branch of mathematics that studies knots, which are closed curves in 3-dimensional space.
Number of Questions: 15
Created by:
Tags: knot theory mathematics topology
Start the Quiz
Attempted 0/15 Correct 0 Score 0
‹
›

What is the simplest knot?

  1. Unknot

  2. Torus Knot

  3. Trefoil Knot

  4. Figure-Eight Knot

Show answer
Correct Option: A
Explanation:

The unknot is a knot that can be continuously deformed into a circle without passing through itself.

What is the name of the knot that is formed by tying a simple overhand knot?

  1. Unknot

  2. Torus Knot

  3. Trefoil Knot

  4. Figure-Eight Knot

Show answer
Correct Option: C
Explanation:

The trefoil knot is the simplest non-trivial knot, meaning that it cannot be continuously deformed into an unknot without passing through itself.

Which of the following is a knot invariant?

  1. Knot type

  2. Crossing number

  3. Genus

  4. Unknotting number

Show answer
Correct Option: A
Explanation:

Knot type is a knot invariant, meaning that it is a property that is preserved under continuous deformations of the knot.

What is the crossing number of a knot?

  1. The number of times the knot crosses itself

  2. The number of components in the knot

  3. The genus of the knot

  4. The unknotting number of the knot

Show answer
Correct Option: A
Explanation:

The crossing number of a knot is the minimum number of times that the knot crosses itself.

What is the genus of a knot?

  1. The number of times the knot crosses itself

  2. The number of components in the knot

  3. The number of holes in the knot's complement

  4. The unknotting number of the knot

Show answer
Correct Option: C
Explanation:

The genus of a knot is the number of holes in the knot's complement, which is the 3-ball minus the interior of the knot.

What is the unknotting number of a knot?

  1. The number of times the knot crosses itself

  2. The number of components in the knot

  3. The genus of the knot

  4. The minimum number of crossing changes required to unknot the knot

Show answer
Correct Option: D
Explanation:

The unknotting number of a knot is the minimum number of crossing changes required to unknot the knot.

What is the Alexander polynomial of a knot?

  1. A polynomial that is associated with a knot

  2. A knot invariant

  3. A knot type

  4. A crossing number

Show answer
Correct Option: A
Explanation:

The Alexander polynomial is a polynomial that is associated with a knot and is a knot invariant.

What is the Jones polynomial of a knot?

  1. A polynomial that is associated with a knot

  2. A knot invariant

  3. A knot type

  4. A crossing number

Show answer
Correct Option: A
Explanation:

The Jones polynomial is a polynomial that is associated with a knot and is a knot invariant.

What is the HOMFLY polynomial of a knot?

  1. A polynomial that is associated with a knot

  2. A knot invariant

  3. A knot type

  4. A crossing number

Show answer
Correct Option: A
Explanation:

The HOMFLY polynomial is a polynomial that is associated with a knot and is a knot invariant.

What is the Kauffman bracket of a knot?

  1. A polynomial that is associated with a knot

  2. A knot invariant

  3. A knot type

  4. A crossing number

Show answer
Correct Option: B
Explanation:

The Kauffman bracket is a knot invariant that is defined using a skein relation.

What is the Conway knot?

  1. A knot that is named after John Horton Conway

  2. A knot that is formed by tying a simple overhand knot

  3. A knot that has a crossing number of 11

  4. A knot that has a genus of 2

Show answer
Correct Option: A
Explanation:

The Conway knot is a knot that is named after John Horton Conway and is a knot that has a crossing number of 11 and a genus of 2.

What is the Gordian knot?

  1. A knot that is said to have been tied by King Gordius

  2. A knot that is impossible to untie

  3. A knot that has a crossing number of 13

  4. A knot that has a genus of 3

Show answer
Correct Option: A
Explanation:

The Gordian knot is a knot that is said to have been tied by King Gordius and was said to be impossible to untie.

What is the trefoil knot?

  1. A knot that is formed by tying a simple overhand knot

  2. A knot that has a crossing number of 3

  3. A knot that has a genus of 1

  4. All of the above

Show answer
Correct Option: D
Explanation:

The trefoil knot is a knot that is formed by tying a simple overhand knot, has a crossing number of 3, and has a genus of 1.

What is the figure-eight knot?

  1. A knot that is formed by tying a figure-eight knot

  2. A knot that has a crossing number of 4

  3. A knot that has a genus of 1

  4. All of the above

Show answer
Correct Option: D
Explanation:

The figure-eight knot is a knot that is formed by tying a figure-eight knot, has a crossing number of 4, and has a genus of 1.

What is the Whitehead link?

  1. A link that is formed by linking two unknots

  2. A link that has a linking number of 0

  3. A link that has a genus of 1

  4. All of the above

Show answer
Correct Option: D
Explanation:

The Whitehead link is a link that is formed by linking two unknots, has a linking number of 0, and has a genus of 1.

- Hide questions
ADVERTISEMENT

Find more quizzes from top tags

general knowledge
3615 Quizzes
119858 Questions
 technology
307 Quizzes
36705 Questions
 sports
963 Quizzes
19148 Questions
 history
1187 Quizzes
13475 Questions
 physics
598 Quizzes
13441 Questions
 biology
1160 Quizzes
12174 Questions
 science & technology
551 Quizzes
11015 Questions
 chemistry
490 Quizzes
9892 Questions
 maths
518 Quizzes
9324 Questions
 softskills
0 Quizzes
7131 Questions