| Type of Document |
Dissertation |
| Author |
Egedy, Charles Richard
|
| Author's Email Address |
cegedy1@tigers.lsu.edu |
| URN |
etd-11042009-151333 |
| Title |
The Extended Picture Group, With Applications to Line Arrangement Complements |
| Degree |
Doctor of Philosophy (Ph.D.) |
| Department |
Mathematics |
| Advisory Committee |
| Advisor Name |
Title |
| Cohen, Daniel |
Committee Chair |
| Hofmann, Jerome |
Committee Member |
| Oporowski, Bogdan |
Committee Member |
| Sengupta, Ambar |
Committee Member |
| Smolinsky, Lawrence |
Committee Member |
| Busch, Konstantin |
Dean's Representative |
|
| Keywords |
- algebraic topology
- higher homotopy
|
| Date of Defense |
2009-10-23 |
| Availability |
unrestricted |
Abstract
We obtain the picture group as the quotient with a torsion subgroup, of an extended picture group, which is isomorphic to the kernel of a precrossed module homomorphism. In addition to expanding the notion of a picture group, the new formulation gives a natural way to construct homomorphisms between picture groups by describing deformations of one-vertex subpictures. The extended picture group thus provides a convenient way to describe generators for the second homotopy group of line arrangement complements as well as homomorphisms between these groups. In particular, we show that the homomorphisms relate to a lattice structure corresponding roughly to the condition of being more nearly in general position. Examples include generators for Falk's X2 arrangement and for a generic section of braid arrangement A3. Finally, we demonstrate that the C3 arrangement C(5) is a K(pi; 1) space.
|
| Files |
| Filename |
Size |
Approximate Download Time
(Hours:Minutes:Seconds)
|
| 28.8 Modem |
56K Modem |
ISDN (64 Kb) |
ISDN (128 Kb) |
Higher-speed Access |
| |
Egedy_diss.pdf |
801.53 Kb |
00:03:42 |
00:01:54 |
00:01:40 |
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