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Morse Theory, Milnor Fibers and Minimality of Hyperplane Arrangements
Proceedings of the American Mathematical Society
Vol. 130, No. 9 (Sep., 2002), pp. 2737-2743
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2699692
Page Count: 7
You can always find the topics here!Topics: Hyperplanes, Critical points, Mathematical complements, Morse theory, Mathematical functions, Hypersurfaces, Combinatorics, Mathematical transformations, Mathematical lattices, Algebraic topology
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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-Mac Lane spaces.
Proceedings of the American Mathematical Society © 2002 American Mathematical Society