Complement

The volume conjecture states that a certain limit of the colored Jones polynomial of a knot in the three-dimensional sphere would give the volume of the knot complement. Here the colored Jones polynomial is a generalization of the celebrated Jones polynomial and is defined by using a so-called R-matrix that is associated with the N-dimensional representation of the Lie algebra sl(2;C). The volume conjecture was first stated by R. Kashaev in terms of his own invariant defined by using the quantum dilogarithm. Later H. Murakami and J. Murakami proved that Kashaev’s invariant is nothing but the N-dimensional colored Jones polynomial evaluated at the Nth root of unity. Then the volume conjecture turns out to be a conjecture that relates an algebraic object, the colored Jones polynomial, with a geometric object, the volume.

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Byte conversion - Dec, bin, oct, hex conversion - Signed number representations: Signed magnitude, One's complement, Two's complement - Bitwise operations - Shift and rotate bits - Password generation - Random number generation - Base 64 encoding / decoding - URL encoding / decoding - MD5, SHA, CRC-32 hash generation - Unix Timestamp conversion - POE calculation - Subnet calculation - Data transfer time - Wake on lan - RGB/HEX conversion

All tools present
Byte conversion - Dec, bin, oct, hex conversion - Signed number representations: Signed magnitude, One's complement, Two's complement - Bitwise operations - Shift and rotate bits - Password generation - Random number generation - Base 64 encoding / decoding - URL encoding / decoding - MD5, SHA, CRC-32 hash generation - Unix Timestamp conversion - POE calculation - Subnet calculation - Data transfer time - Wake on lan - RGB/HEX conversion

All tools present
Byte conversion - Dec, bin, oct, hex conversion - Signed number representations: Signed magnitude, One's complement, Two's complement - Bitwise operations - Shift and rotate bits - Password generation - Random number generation - Base 64 encoding / decoding - URL encoding / decoding - MD5, SHA, CRC-32 hash generation - Unix Timestamp conversion - POE calculation - Subnet calculation - Data transfer time - Wake on lan - RGB/HEX conversion

All tools present
Byte conversion - Dec, bin, oct, hex conversion - Signed number representations: Signed magnitude, One's complement, Two's complement - Bitwise operations - Shift and rotate bits - Password generation - Random number generation - Base 64 encoding / decoding - URL encoding / decoding - MD5, SHA, CRC-32 hash generation - Unix Timestamp conversion - POE calculation - Subnet calculation - Data transfer time - Wake on lan - RGB/HEX conversion

All tools present
Byte conversion - Dec, bin, oct, hex conversion - Signed number representations: Signed magnitude, One's complement, Two's complement - Bitwise operations - Shift and rotate bits - Password generation - Random number generation - Base 64 encoding / decoding - URL encoding / decoding - MD5, SHA, CRC-32 hash generation - Unix Timestamp conversion - POE calculation - Subnet calculation - Data transfer time - Wake on lan - RGB/HEX conversion

This monograph derives direct and concrete relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements. Under mild diagrammatic hypotheses, we prove that the growth of the degree of the colored Jones polynomials is a boundary slope of an essential surface in the knot complement.