A toric arrangement is a finite set of hypersurfaces in a complex torus, every hypersurface being the kernel of a character. In the present paper, we build a CW-complex homotopy equivalent to the arrangement complement, with a combinatorial description similar to that of the well-known Salvetti complex. If the toric arrangement is defined by a Weyl group, we also provide an algebraic description, very handy for cohomology computations. In the last part, we give a description in terms of tableaux for a toric arrangement appearing in robotics. © 2010 Elsevier B.V.
MOCI L, SETTEPANELLA S (2011). The homotopy type of toric arrangements. JOURNAL OF PURE AND APPLIED ALGEBRA, 215(8), 1980-1989 [10.1016/j.jpaa.2010.11.008].
The homotopy type of toric arrangements
MOCI L;
2011
Abstract
A toric arrangement is a finite set of hypersurfaces in a complex torus, every hypersurface being the kernel of a character. In the present paper, we build a CW-complex homotopy equivalent to the arrangement complement, with a combinatorial description similar to that of the well-known Salvetti complex. If the toric arrangement is defined by a Weyl group, we also provide an algebraic description, very handy for cohomology computations. In the last part, we give a description in terms of tableaux for a toric arrangement appearing in robotics. © 2010 Elsevier B.V.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
