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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Morse theory, Milnor fibers and minimality of hyperplane arrangements


Author: Richard Randell
Journal: Proc. Amer. Math. Soc. 130 (2002), 2737-2743
MSC (2000): Primary 52C35, 55Q52; Secondary 14N20, 32S22
Published electronically: February 4, 2002
MathSciNet review: 1900880
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Abstract: Through the study of Morse theory on the associated Milnor fiber, we show that complex hyperplane arrangement complements are minimal. That is, the complement of any complex hyperplane arrangement has the homotopy type of a CW-complex in which the number of $p$-cells equals the $p$-th betti number. Combining this result with recent work of Papadima and Suciu, one obtains a characterization of when arrangement complements are Eilenberg-MacLane spaces.


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Additional Information

Richard Randell
Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
Email: randell@math.uiowa.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06412-2
PII: S 0002-9939(02)06412-2
Keywords: Hyperplane arrangement, Milnor fiber, Morse theory
Received by editor(s): November 29, 2000
Received by editor(s) in revised form: April 16, 2001
Published electronically: February 4, 2002
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2002 American Mathematical Society