A polynomial invariant for plane curve complements: Krammer polynomials

Mehmet Aktaş, Serdar Cellat, and Hubeyb Gurdogan

Journal of Singularities
volume 17 (2018), 58-69

Received: 15 October 2017. Received in revised form: 16 February 2018.

DOI: 10.5427/jsing.2018.17c

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Abstract:

We use the Krammer representation of the braid group in Libgober's invariant and construct a new multivariate polynomial invariant for curve complements: Krammer polynomial. We show that the Krammer polynomial of an essential braid is equal to zero. We also compute the Krammer polynomials of some certain n-gonal curves.


Keywords:

Braid monodromy, n-gonal curves, Krammer representation, Krammer polynomial


2010 Mathematical Subject Classification:

Primary 14H30, 20F36; Secondary 14H45


Author(s) information:

Mehmet Aktaş Serdar Cellat Hubeyb Gurdogan
Department of Mathematics and Statistics Department of Mathematics Department of Mathematics
University of Central Oklahoma Florida State University Florida State University
Edmond, Oklahoma 73003 Tallahassee, Florida 32306 Tallahassee, Florida 32306
USA USA USA
email: maktas@uco.edu email: scellat@math.fsu.edu email: hgurdoga@math.fsu.edu