2011/12/16 by Funda Gültepe, Gültepe, Funda
Mathematics · #20F28 #20F65 (Secondary) #57M07 (Primary) 20E05 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:20E05 #msc:20F28 #msc:20F65 #msc:57M07
paper · pdf · doi:10.48550/arxiv.1112.3693
14 pages, 4 figures
arxiv created 2012/06/08 · arxiv updated 2012/06/12
The fundamental group of M = \sharpn (S2× S1) is Fn, the free group with n generators. There is a 1-1 correspondence between the equivalence classes of ℤ-- splittings of Fn and homotopy classes of embedded essential tori in M. We define and prove a local notion of minimal intersection of a torus with respect to a maximal sphere system in M, which generalizes Hatcher's work \citeH1 on 2-spheres in the same manifold.