We prove that the rational completion of the Alexander invariant of a
1-formal group G is determined by the holonomy Lie algebra of G. One
obtains in this way local analytic isomorphisms between germs of
characteristics and resonance varieties of G. For fundamental groups of
smooth complex varieties, this leads to new restrictions on associated
resonance varieties, thereby answering a question of Serre. When applied
to Artin groups, this gives an explicit characterization of right-angled
groups realized by smooth varieties, thus extending work by Kapovich and
Millson.

Keywords:

Fundamental Group; Smooth Complex Variety; Alexander Invariant; Characteristic Variety; Resonance Variety; Artin Groups.

Lecture #10694

Need help? Visit our help pages at http://www.msri.org/communications/vmath/hints

Supplements

Right click on the link and "Save As..." to save to your local computer.

• 10694.pdf (0.2 MB)

Left click on thumbnail to see a larger image.

Streaming Video

This is a high quality streaming video encoded with MPEG-4 and with 640x480 resolution.

Windows and Mac users, QuickTime 6.5 or later required
Linux users, please see our Linux Help Page on how to view our streaming videos

Follow this link to --- Watch the Video Now Via Streaming Video ---

Download QuickTime File

You can download the QuickTime file here. Right click on the link and "Save As..." to save to your local computer.

• 10694-10694-QuickTime.mov (206 MB)

Create a DVD

You can download the video and audio files here. Please note that you need both files to create a DVD. Right click on the link and "Save As..." to save to your local computer. You can find instructions on how to create a DVD on our help page at http://www.msri.org/communications/vmath/author

• 10694-10694-DVD PCM Audio.aiff (304 MB - Audio Only)
• 10694-10694-MPEG-2 120min High Quality Encode.m2v (692 MB - Video Only)

Buy the DVD

If none of the options work for you, you can always buy the DVD of this lecture.

If you would like to purchase a copy of this video for $15+shipping, please Click Here!

See more of our Streaming Videos on our main VMath - Streaming Video page.