Abstract
We study torsion properties of the twisted Alexander modules of the affine complement M of a complex essential hyperplane arrangement, as well as those of punctured stratified tubular neighborhoods of complex essential hyperplane arrangements. We investigate divisibility properties between the twisted Alexander polynomials of the two spaces, compute the (first) twisted Alexander polynomial of a punctured stratified tubular neighborhood of an essential line arrangement, and study the possible roots of the twisted Alexander polynomials of both the complement and the punctured stratified tubular neighborhood of an essential hyperplane arrangement in higher dimensions. We apply our results to distinguish non-homeomorphic homotopy equivalent arrangement complements. We also relate the twisted Alexander polynomials of M with the corresponding twisted homology jump loci.
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Acknowledgements
The author would like to thank Laurenţiu Maxim for all of his guidance and support during this project, as well as the referee for their helpful comments. She would also like to acknowledge Enrique Artal-Bartolo, José Ignacio Cogolludo-Agustín, and Miguel Ángel Marco-Buzunáriz for the interesting discussions we had about this topic.
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Elduque, E. Twisted Alexander modules of hyperplane arrangement complements. RACSAM 115, 70 (2021). https://doi.org/10.1007/s13398-021-01008-4
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DOI: https://doi.org/10.1007/s13398-021-01008-4