$k$-Parabolic subspace arrangements
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- by Hélène Barcelo, Christopher Severs and Jacob A. White PDF
- Trans. Amer. Math. Soc. 363 (2011), 6063-6083 Request permission
Abstract:
In this paper, we study $k$-parabolic arrangements, a generalization of $k$-equal arrangements for finite real reflection groups. When $k=2$, these arrangements correspond to the well-studied Coxeter arrangements. Brieskorn (1971) showed that the fundamental group of the complement, over $\mathbb {C}$, of the type $W$ Coxeter arrangement is isomorphic to the pure Artin group of type $W$. Khovanov (1996) gave an algebraic description for the fundamental group of the complement, over $\mathbb {R}$, of the $3$-equal arrangement. We generalize Khovanov’s result to obtain an algebraic description of the fundamental groups of the complements of $3$-parabolic arrangements for arbitrary finite reflection groups. Our description is a real analogue to Brieskorn’s description.References
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Additional Information
- Hélène Barcelo
- Affiliation: School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287 – and – Mathematical Sciences Research Institute, Berkeley, California 94720
- Email: hbarcelo@msri.org
- Christopher Severs
- Affiliation: Mathematical Sciences Research Institute, Berkeley, California 94720
- Address at time of publication: Department of Mathematics, Reykjavík University, Menntavegur 1, IS 101, Reykjavík, Iceland
- Email: csevers@msri.org
- Jacob A. White
- Affiliation: School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287
- Address at time of publication: Mathematical Sciences Research Institute, 17 Gauss Way, Berkeley, California 94720
- Email: jacob.a.white@asu.edu, jawhite@msri.org
- Received by editor(s): September 3, 2009
- Received by editor(s) in revised form: February 24, 2010
- Published electronically: June 17, 2011
- Additional Notes: The second author was partially supported by NSF grant DMS-0441170, administered by the Mathematical Sciences Research Institute, while the author was in residence during the Complementary Program, Fall 2009–Spring 2010. We thank the institute for its support.
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 363 (2011), 6063-6083
- MSC (2010): Primary 52C35, 05E99
- DOI: https://doi.org/10.1090/S0002-9947-2011-05336-5
- MathSciNet review: 2817419