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 = {Kitano, Teruaki}, title = {Introduction to twisted {Alexander} polynomials and related topics}, booktitle = {Winter Braids V (Pau, 2015)}, series = {Winter Braids Lecture Notes}, note = {talk:4}, pages = {1--35}, publisher = {Winter Braids School}, year = {2015}, doi = {10.5802/wbln.10}, mrnumber = {3705876}, zbl = {1422.57037}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/wbln.10/} }
TY - JOUR AU - Kitano, Teruaki TI - Introduction to twisted Alexander polynomials and related topics BT - Winter Braids V (Pau, 2015) AU - Collectif T3 - Winter Braids Lecture Notes N1 - talk:4 PY - 2015 SP - 1 EP - 35 PB - Winter Braids School UR - http://archive.numdam.org/articles/10.5802/wbln.10/ DO - 10.5802/wbln.10 LA - en ID - WBLN_2015__2__A4_0 ER -
%0 Journal Article %A Kitano, Teruaki %T Introduction to twisted Alexander polynomials and related topics %B Winter Braids V (Pau, 2015) %A Collectif %S Winter Braids Lecture Notes %Z talk:4 %D 2015 %P 1-35 %I Winter Braids School %U http://archive.numdam.org/articles/10.5802/wbln.10/ %R 10.5802/wbln.10 %G en %F WBLN_2015__2__A4_0
Kitano, Teruaki. Introduction to twisted Alexander polynomials and related topics, in Winter Braids V (Pau, 2015), Winter Braids Lecture Notes (2015), Talk no. 4, 35 p. doi : 10.5802/wbln.10. http://archive.numdam.org/articles/10.5802/wbln.10/
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