Homotopy Types of Complements of 2-arrangements in R
نویسندگان
چکیده
We study the homotopy types of complements of arrangements of n transverse planes in R4, obtaining a complete classification for n ≤ 6, and lower bounds for the number of homotopy types in general. Furthermore, we show that the homotopy type of a 2-arrangement in R4 is not determined by the cohomology ring, thereby answering a question of Ziegler. The invariants that we use are derived from the characteristic varieties of the complement. The nature of these varieties illustrates the difference between real and complex arrangements.
منابع مشابه
ar X iv : m at h / 97 12 25 1 v 2 [ m at h . G T ] 1 4 A ug 1 99 8 HOMOTOPY TYPES OF COMPLEMENTS OF 2 - ARRANGEMENTS IN R 4
We study the homotopy types of complements of arrangements of n transverse planes in R, obtaining a complete classification for n ≤ 6, and lower bounds for the number of homotopy types in general. Furthermore, we show that the homotopy type of a 2-arrangement in R is not determined by the cohomology ring, thereby answering a question of Ziegler. The invariants that we use are derived from the c...
متن کاملDaniel Matei And
We study the homotopy types of complements of arrangements of n transverse planes in R, obtaining a complete classification for n ≤ 6, and lower bounds for the number of homotopy types in general. Furthermore, we show that the homotopy type of a 2-arrangement in R is not determined by the cohomology ring, thereby answering a question of Ziegler. The invariants that we use are derived from the c...
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تاریخ انتشار 1998