The lower algebraic k-theory of virtually cyclic subgroups of the braid groups of the sphere and of ZB4(S2) / John Guaschi, Daniel Juan-Pineda, Silvia Millán López.

Intro; Preface; References; Acknowledgements; Reference; Contents; 1 Introduction; References; 2 Lower Algebraic K-Theory of the Finite Subgroups of Bn(); 2.1 Classification of the Virtually Cyclic Subgroups of Bn(); 2.2 Conjugacy Classes of Binary Polyhedral Groups; 2.3 Whitehead Groups of the Finite Subgroups of Bn(); 2.4 widetildeK0(mathbbZ[G]) for the Finite Subgroups of Bn(); 2.5 K-1(mathbbZ[G]) for the Finite Subgroups of Bn(); 2.5.1 Torsion of K-1(mathbbZ[G]) for Finite Subgroups of Bn(); 2.5.2 The Rank of K-1(mathbbZ[G]) for the Finite Subgroups of Bn()

2.6 The Lower Algebraic K-Theory of the Finite Subgroups of Bn() for 4leqnleq11References; 3 The Braid Group B4(), and the Conjugacy Classes of Its Maximal Virtually Cyclic Subgroups; 3.1 Generalities about B4(); 3.2 Maximal Virtually Cyclic Subgroups of B4(); 3.2.1 Proof of Parts (a) and (b) of Theorem 41; 3.2.2 Proof of Parts (c) and (d) of Theorem 41; 3.2.3 Proof of the Existence of Maximal Subgroups timesmathbbZ in Part (c) of Theorem 41; 3.3 Conjugacy Classes of Maximal Infinite Virtually Cyclic Subgroups in B4(); References

4 Lower Algebraic K-Theory Groups of the Group Ring mathbbZ[B4()]4.1 The Lower K-Theory of Infinite Virtually Cyclic Groups; 4.2 Preliminary K-Theoretical Calculations for mathbbZ[B4()]; 4.3 Nil Group Computations; References; A The Fibred Isomorphism Conjecture; The Setup; The Conjecture; Appendix B Braid Groups; References