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Generalizing the Kneser Conjecture

Gerrit Smith, SLU

  • PhD Oral Exam
  • Geometry/ Topology Seminar
  • Topology Seminar
When Mon, Nov 23, 2015
from 11:00 AM to 12:00 PM
Where 323 Ritter Hall (Mac Lab)
Contact Name
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The Kneser Conjecture says that if a closed connected 3-manifold M has π1(M)=G1 * G2, then there exist 3-manifolds M1 and M2 such that π1(Mi)=Gi and M=M1#M2. Hillman has generalized this to 4-manifolds at the expense of introducing stabilizing S2 × S2 factors to M. More precisely, if a closed connected 4-manifold M has π1(M)=G1 * G2, then there exist 4-manifolds M1 and M2 such that π1(Mi)=Gi and M#n(S2 × S2)=M 1#M2 for some nonnegative integer n.

This talk will review these results, and then consider a generalization of these theorems to 3- and 4-manifolds with fundamental groups which are amalgamated free products. The 3-dimensional case for amalgamated products has been done by Feustel. The talk will end with a discussion of progress made in the case that the amalgamation is over a cyclic group of prime order.

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