Topology

Notes from the classroom(taught by professor Yulan Qing)

Exercises with solutions:

1. 1. 3-regular and 4-regular graphs that are not isomorphic

   2. Characterization of finite trees copy

   3. Dehn twist is not 1 in MAP(S) and is infinite order

   4. Every action of a finite group on a tree has a global fixed point

   5. Integers acts on the unit circle freely if-f the angle is irrational

   6. Is the additive group of rational numbers free abelian group?

   7. Let S1 and S2 be finite generating sets of a group G, then Cay(G,S1) is quasi-isometric Cay(G,S2)

   8. The additive group of rational numbers is not finitely generated

   9. The multiplicative group of rational numbers is not finitely generated

Books:

1. 1. Geometric Group Theory: An Introduction, C. Löh

   2. A Primer on Mapping Class Groups, B. Farb and D. Margalt

   3. Graphs and Matrices, R. B. Bapat

   4. Trees, Jean-Pierre Serre