**UM Math Graduate Student Seminar**

Chris Anderson*University of Miami ***will present**

**The Prime and JSJ Decompositions**

Friday, September 21st, 2018, 5:00pm

Ungar Building Room 402**Abstract:**

One of the basic aims of low dimensional and geometric topology is to

reduce the difficulty of analyzing complicated manifolds by dividing them

into several smaller pieces that are easier to understand. We will talk

about two such methods. The first of these will be the prime decomposition

of compact orientable 3-manifolds due to Kneser and Milnor. The second of

these will be the toral decomposition of irreducible, orientable closed

3-manifolds due to Johannson and Jaco-Shalen, which we will use

asmotivation for an introduction to Seifert fibered manifolds.