A vanishing theorem for twisted Alexander polynomials with applications to symplectic 4-manifolds

Friedl, Stefan, and Vidussi, Stefano. "A vanishing theorem for twisted Alexander polynomials with applications to symplectic 4-manifolds." Journal of the European Mathematical Society 015.6 (2013): 2027-2041. <http://eudml.org/doc/277433>.

@article{Friedl2013,
abstract = {In this paper we show that given any 3-manifold $N$ and any non-fibered class in $H^1(N;Z)$ there exists a representation such that the corresponding twisted Alexander polynomial is zero. We obtain this result by extending earlier work of ours and by combining this with recent results of Agol and Wise on separability of 3-manifold groups. This result allows us to completely classify symplectic 4-manifolds with a free circle action, and to determine their symplectic cones.},
author = {Friedl, Stefan, Vidussi, Stefano},
journal = {Journal of the European Mathematical Society},
keywords = {twisted Alexander polynomials; fibered 3-manifolds; symplectic 4-manifolds; twisted Alexander polynomials; fibered 3-manifolds; symplectic 4-manifolds},
language = {eng},
number = {6},
pages = {2027-2041},
publisher = {European Mathematical Society Publishing House},
title = {A vanishing theorem for twisted Alexander polynomials with applications to symplectic 4-manifolds},
url = {http://eudml.org/doc/277433},
volume = {015},
year = {2013},
}

TY - JOUR
AU - Friedl, Stefan
AU - Vidussi, Stefano
TI - A vanishing theorem for twisted Alexander polynomials with applications to symplectic 4-manifolds
JO - Journal of the European Mathematical Society
PY - 2013
PB - European Mathematical Society Publishing House
VL - 015
IS - 6
SP - 2027
EP - 2041
AB - In this paper we show that given any 3-manifold $N$ and any non-fibered class in $H^1(N;Z)$ there exists a representation such that the corresponding twisted Alexander polynomial is zero. We obtain this result by extending earlier work of ours and by combining this with recent results of Agol and Wise on separability of 3-manifold groups. This result allows us to completely classify symplectic 4-manifolds with a free circle action, and to determine their symplectic cones.
LA - eng
KW - twisted Alexander polynomials; fibered 3-manifolds; symplectic 4-manifolds; twisted Alexander polynomials; fibered 3-manifolds; symplectic 4-manifolds
UR - http://eudml.org/doc/277433
ER -