The Complex of Non-separating embedded spheres
Suhas Pandit

TL;DR
This paper demonstrates that the automorphism group of the complex of non-separating embedded spheres in a specific 3-manifold is isomorphic to the outer automorphism group of a free group, revealing a deep connection between topology and algebra.
Contribution
It establishes an isomorphism between the automorphism group of a sphere complex in a 3-manifold and the outer automorphism group of a free group, extending understanding of manifold automorphisms.
Findings
Aut(NS(M)) is isomorphic to Out(F_n) for n > 2
The complex NS(M) encodes algebraic automorphism structures
Provides a topological model for Out(F_n)
Abstract
For n >2, we shall show that the group Aut(NS(M)) of simplicial automorphisms of the complex NS(M) of non-separating embedded spheres in the manifold M,connected sum of n copies of S^2 X S^1, isomorphic to the group Out(F_n) of outer automorphisms of the free group F_n, where is identified with the fundamental group of M up to conjugacy of the base point in M.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Geometric Analysis and Curvature Flows
