2001/08/03 by Jennifer Schultens, Schultens, Jennifer
Mathematics · #57N10 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57N10
paper · pdf · doi:10.48550/arxiv.math/0108028
21 pages, 17 figures
arxiv created 2006/05/31 · arxiv updated 2009/11/30
Given a 3-manifold M containing an incompressible surface Q, we obtain an inequality relating the Heegaard genus of M and the Heegaard genera of the components of M - Q. Here the sum of the genera of the components of M - Q is bounded above by a linear expression in terms of the genus of M, the Euler characteristic of Q and the number of parallelism classes of essential annuli for which representatives can be simultaneously imbedded in the components of M - Q.