This article is based on the lectures in the Winter Braids V (Pau, February 2015). We introduce some studies of twisted Alexander polynomials to non-experts through many concrete examples. In this article we follow the definition of the twisted Alexander polynomial by Wada, which can be defined for a finitely presented group with an epimorphism onto a free abelian group. The main tool is FoxÕs free calculus. In the last two sections we discuss some applications on the fiberedness of a knot and the existence of epimorphisms between knot groups.
@article{WBLN_2015__2__A4_0, author = {Teruaki Kitano}, title = {Introduction to twisted {Alexander} polynomials and related topics}, journal = {Winter Braids Lecture Notes}, note = {talk:4}, pages = {1--35}, publisher = {Winter Braids School}, volume = {2}, year = {2015}, doi = {10.5802/wbln.10}, mrnumber = {3705876}, zbl = {1422.57037}, language = {en}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/wbln.10/} }
TY - JOUR AU - Teruaki Kitano TI - Introduction to twisted Alexander polynomials and related topics JO - Winter Braids Lecture Notes N1 - talk:4 PY - 2015 SP - 1 EP - 35 VL - 2 PB - Winter Braids School UR - https://proceedings.centre-mersenne.org/articles/10.5802/wbln.10/ DO - 10.5802/wbln.10 LA - en ID - WBLN_2015__2__A4_0 ER -
%0 Journal Article %A Teruaki Kitano %T Introduction to twisted Alexander polynomials and related topics %J Winter Braids Lecture Notes %Z talk:4 %D 2015 %P 1-35 %V 2 %I Winter Braids School %U https://proceedings.centre-mersenne.org/articles/10.5802/wbln.10/ %R 10.5802/wbln.10 %G en %F WBLN_2015__2__A4_0
Teruaki Kitano. Introduction to twisted Alexander polynomials and related topics. Winter Braids Lecture Notes, Volume 2 (2015), Talk no. 4, 35 p. doi : 10.5802/wbln.10. https://proceedings.centre-mersenne.org/articles/10.5802/wbln.10/
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