Hyperplane Arrangements by Alexandru Dimca

Author:Alexandru Dimca
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Exercise 5.2

Show that for the Boolean arrangement , the action of the monodromy on the cohomology, , is the identity.

Exercise 5.3

Let be a central, essential, indecomposable arrangement in , for some . Show that the action of the monodromy on the cohomology, , cannot be the identity.

Exercise 5.4

Using Theorems 4.​3 and 5.1, show the following.

(i)Consider the central arrangement in defined by . Let be any central arrangement in such that the intersection lattice is isomorphic to the intersection lattice . Show that the corresponding complements and (resp. the corresponding Milnor fibers and ) are diffeomorphic. Compute the Alexander polynomials for the monodromy operator of the arrangement .

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