On the signature of positive braids and adjacency for torus knots

Feller, Peter (2014). On the signature of positive braids and adjacency for torus knots. (Dissertation, Universität Bern, Philosophisch-naturwissenschaftliche Fakultät, Mathematisches Institut)

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The objects of study in this thesis are knots. More precisely, positive braid knots, which include algebraic knots and torus knots. In the first part of this thesis, we compare two classical knot invariants - the genus g and the signature σ - for positive braid knots. Our main result on positive braid knots establishes a linear lower bound for the signature in terms of the genus. In the second part of the thesis, a positive braid approach is applied to the study of the local behavior of polynomial functions from the complex affine plane to the complex numbers. After endowing polynomial function germs with a suitable topology, the adjacency problem arises: for a fixed germ f, what classes of germs g can be found arbitrarily close to f? We introduce two purely topological notions of adjacency for knots and discuss connections to algebraic notions of adjacency and the adjacency problem.

Item Type:

Thesis (Dissertation)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Feller, Peter and Baader, Sebastian

Subjects:

500 Science > 510 Mathematics

Language:

English

Submitter:

Igor Hammer

Date Deposited:

06 Oct 2014 15:03

Last Modified:

09 Dec 2014 08:57

URN:

urn:nbn:ch:bel-bes-1461

Additional Information:

e-dissertation (edbe)

BORIS DOI:

10.7892/boris.58685

URI:

https://boris.unibe.ch/id/eprint/58685

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