Morse theory, Milnor fibers and minimality of hyperplane arrangements

By R. Randell. 2000

59 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b3b7876e89cac120ca77182845da9a4b6cfaf433

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Milnor numbers of projective hypersurfaces and the chromatic polynomial of graphs (2010, methodology): “We adapt an argument of Randell [30] to prove the”
Hyperplane arrangements and Lefschetz's hyperplane section theorem (2005, background): “Recently Dimca-Papadima [1] and Randell [2] proved that the complement M(A) of a complex hyperplane arrangement A in C is homotopy equivalent to a minimal CWcomplex, namely, a CW-complex whose number of k-cells is equal to its k-th betti number for each k ≥ 0.”