Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations

TL;DR: For every finite Abelian group and integer, the authors construct a finite presented group defined by explicit generators and relations such that its centre is isomorphic to the given integer, and for every integer,

TL;DR: For genus 2 Torelli functions, the zero locus of any such function is homotopy equivalent to an infinite wedge of 2-spheres as discussed by the authors, where σ denotes rank 2 Siegel space.

TL;DR: The existence of nontrivial homotopy torus knot spaces is established as a corollary to the Theorem as discussed by the authors, where the authors show that a 3-mainfold is irreducible if every embedded 2-sphere bounds a 3cell.