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Autor:
Cohen, Daniel C., Orlik, Peter
Publikováno v:
Pure Appl. Math. Q. 2 (2006), 673-697
This paper is a survey of our work based on the stratified Morse theory of Goresky and MacPherson. First we discuss the Morse theory of Euclidean space stratified by an arrangement. This is used to show that the complement of a complex hyperplane arr
Externí odkaz:
http://arxiv.org/abs/math/0603471
Autor:
Cohen, Daniel C., Orlik, Peter
Publikováno v:
Comment. Math. Helv. 81 (2006), 883-909
An arrangement is a finite set of hyperplanes in a finite dimensional complex affine space. A complex rank one local system on the arrangement complement is determined by a set of complex weights for the hyperplanes. We study the Gauss-Manin connecti
Externí odkaz:
http://arxiv.org/abs/math/0502111
Autor:
Cohen, Daniel C., Orlik, Peter
Publikováno v:
Trans. Amer. Math. Soc. 357 (2005), 3031-3050
We study the Gauss-Manin connection for the moduli space of an arrangement of complex hyperplanes in the cohomology of a complex rank one local system. We define formal Gauss-Manin connection matrices in the Aomoto complex and prove that, for all arr
Externí odkaz:
http://arxiv.org/abs/math/0307210
Autor:
Cohen, Daniel C., Orlik, Peter
Publikováno v:
Amer. J. Math. 127 (2005), 569-594
We study the Gauss-Manin connection for the moduli space of an arrangement of complex hyperplanes in the cohomology of a nonresonant complex rank one local system. Aomoto and Kita determined this Gauss-Manin connection for arrangements in general pos
Externí odkaz:
http://arxiv.org/abs/math/0207114
Autor:
Cohen, Daniel C., Orlik, Peter
Publikováno v:
Compositio Math. 136 (2003), 299-316
We construct a formal connection on the Aomoto complex of an arrangement of hyperplanes, and use it to study the Gauss-Manin connection for the moduli space of the arrangement in the cohomology of a complex rank one local system. We prove that the ei
Externí odkaz:
http://arxiv.org/abs/math/0105063