Personal tools
 

Realizing Injective Splittings of Stable 4-Manifolds

— filed under:

Gerrit Smith, SLU

What
  • PhD Oral Defense
When Thu, Apr 27, 2017
from 03:10 PM to 04:00 PM
Where 323 Ritter Hall
Contact Name
Attendees PhD Dissertation Defense Committee:
Qayum Khan (chair), Kimberly Druschel, John Kalliongis
Add event to calendar vCal
iCal

A decomposition of a manifold, obtained by cutting along a two-sided codimension-one connected incompressible submanifold, induces a decomposition of the fundamental group as an injective amalgamated product or as an HNN extension.

The converse of this fact, called the realization problem, is discussed.  In every dimension except 4, the realization problem is more-or-less always solvable.  However, in dimension 4 there are splittings of fundamental groups which are not induced by splittings of 4-manifolds.  Often by allowing for stabilization of the 4-manifolds, it is possible to realize splittings of their fundamental groups.

The obstruction to stably realizing a splitting is an equation in a 3-dimensional oriented or spin bordism group, depending on the second Stiefel--Whitney class of the universal cover.  Simple examples of realizable and non-realizable splittings are described.  The proofs of existence and uniqueness are outlined.

« December 2017 »
December
SuMoTuWeThFrSa
12
3456789
10111213141516
17181920212223
24252627282930
31