ALEXANDER INVARIANTS OF COMPLEX HYPERPLANE ARRANGEMENTS
作者： Daniel C. Cohen , Alexander I. Suciu
DOI: 10.1090/S0002-9947-99-02206-0
关键词: Lawrence–Krammer representation 、 Invariant (mathematics) 、 Combinatorics 、 Braid theory 、 Mathematics 、 Homomorphism 、 Monodromy 、 Hyperplane 、 Braid 、 Braid group
摘要: LetA be an arrangement of n complex hyperplanes. The funda- mental group the complement A is determined by a braid monodromy homomorphism, fi : Fs ! Pn. Using Gassner representation pure group, we flnd explicit presentation for Alexander invariant ofA. From this presentation, obtain combinatorial lower bounds ranks Chen groups We also provide criterion when these are attained.
ams.org
unirioja.es
harvard.edu
sci-hub.st 参考文章(24)
Helmut A. Hamm, Lê Dũng Tráng, Un théorème de Zariski du type de Lefschetz Annales Scientifiques De L Ecole Normale Superieure. ,vol. 6, pp. 317- 355 ,(1973) , 10.24033/ASENS.1250
Mark Goresky, Robert MacPherson, Stratified Morse theory ,(1988)
Hiroaki Terao, Peter Orlik, Arrangements of hyperplanes ,(1992)
Alexander I. Suciu, Daniel C. Cohen, The Chen Groups of the Pure Braid Group ,(1995)
Joan S. Birman, Braids, Links, and Mapping Class Groups. ,(1975)
Michael Falk, Richard Randell, The lower central series of a fiber-type arrangement. Inventiones Mathematicae. ,vol. 82, pp. 77- 88 ,(1985) , 10.1007/BF01394780
R.H Crowell, The derived module of a homomorphism Advances in Mathematics. ,vol. 6, pp. 210- 238 ,(1971) , 10.1016/0001-8708(71)90016-8
Richard Randell, Homotopy and group cohomology of arrangements Topology and its Applications. ,vol. 78, pp. 201- 213 ,(1997) , 10.1016/S0166-8641(96)00123-X
Eriko Hironaka, Alexander Stratifications of Character Varieties Annales de l'Institut Fourier. ,vol. 47, pp. 555- 583 ,(1997) , 10.5802/AIF.1573
Michael Falk, The minimal model of the complement of an arrangement of hyperplanes Transactions of the American Mathematical Society. ,vol. 309, pp. 543- 556 ,(1988) , 10.1090/S0002-9947-1988-0929668-7