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5 results for three-braids

Sharp signature bound for positive four-braids derived from three-braids.

problem Optimizing the signature bound for positive four-braids.
method Combining bounds for positive three-braids with Gordon and Litherland's approach to signature via unoriented surfaces and Goeritz forms.
result Improved linear bounds for the signature in terms of the three-genus of closures and first Betti number.

Twisted links are obtained from a base link by starting with a nn-braid representation, choosing several (mm) adjacent strands, and applying one or more twists to the set. Various restrictions may be applied, e.g. the twists may be required to be positive or full twists, or the base braid may be required to have a ce…

2011-08-07abs ↗pdf ↗

Associated with each oriented link is the two variable Homflypt polynomial. The Morton-Franks-Williams (MFW) inequality gives rise to an expression for the Homflypt polynomial with MFW coefficient polynomials. These MFW coefficient polynomials are labelled in a braid-dependent manner and may be zero, but display a numb…

2010-09-26abs ↗pdf ↗

New method calculates colored HOMFLY polynomials for knots drawn as double fat graphs.

problem Calculating HOMFLY polynomials for knots drawn as double fat graphs.
method Using fusion and braiding matrices of four-strand braids, incorporating four-point conformal blocks in WZNW models.
result Conjectured and verified colored HOMFLY polynomials for many knots, including distinguishing and non-distinguisable mutants.