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Topology and homotopy of lattice isomorphic arrangements


Author: Benoît Guerville-Ballé
Journal: Proc. Amer. Math. Soc. 148 (2020), 2193-2200
MSC (2010): Primary 52C30, 32S22, 32Q55, 54F65, 14E25
DOI: https://doi.org/10.1090/proc/14878
Published electronically: January 15, 2020
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Abstract: We prove the existence of lattice isomorphic line arrangements having $ \pi _1$-equivalent or homotopy-equivalent complements and non-homeomorphic embeddings in the complex projective plane. We also provide two explicit examples: one is formed by real-complexified arrangements, while the second is not.


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Additional Information

Benoît Guerville-Ballé
Affiliation: Institute of Mathematics, Polish Academy of Sciences, ul. Sniadeckich 8, 00-656 Warsaw, Poland
Email: benoit.guerville-balle@math.cnrs.fr

DOI: https://doi.org/10.1090/proc/14878
Received by editor(s): November 28, 2018
Received by editor(s) in revised form: September 19, 2019
Published electronically: January 15, 2020
Additional Notes: During this work the author was supported by a JSPS postdoctoral grant and by the postdoctoral grant #2017/15369-0 of the Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP). He is currently supported by the Polish Academy of Sciences.
Communicated by: Kenneth Bromberg
Article copyright: © Copyright 2020 American Mathematical Society