2004/10/04 by Siddhartha Gadgil, Gadgil, Siddhartha
Computer Science · Mathematics · #20E06 #57M05 #57M07 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Topological and Geometric Data Analysis #math.GR #math.GT #msc:20E06 #msc:57M05 #msc:57M07
paper · pdf · doi:10.48550/arxiv.math/0410047
8 pages
arxiv created 2004/10/04 · openalex publication_date 2004/10/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give an algorithm to decide which elements of pi2(S2× S1#...#S2× S1) can be represented by embedded spheres. Such spheres correspond to splittings of the free group on k generators. Equivalently our algorithm decides whether, for a handlebody N, an element in pi2(N,∂ N) can be represented by an embedded disc. We also give an algorithm to decide when classes in π2(S2× S1#...#S2× S1) can be represented by disjoint embedded spheres. We introduce the splitting complex of a free group which is analogous to the complex of curves of a surface. We show that the splitting complex of the free group on k generators embeds in the complex of curves of a surface of genus k as a quasi-convex subset.