Up: Math 227B: Automorphism groups of elementary spaces

Homework List for Math 227B
Automorphism Groups

Assignment: 1 |2 |3

Assignment 1

Due Date: Tuesday January 17th

Assignment 2

Due Date: Thursday January 26th (new date)
  • Do: Use Whitehead's algorithm to prove that {xy, zyz, ZYYX} is a basis. Show your intermediate steps! Next, write it as a product of Nielsen transformations. Use the ab notation introduced in class.
  • Do: Convert the presentation in Gersten's article to our notation and then verify and/or correct each of the relations.
  • Optional: For the computer inclined, write a computer program to carry out Whitehead's algorithm on a set of words.

Assignment 3

Due Date: Thursday February 9th
  • Calculate: the neighborhood of the standard rose labeled x,y,z in the reduced spine of outer space for the free group of rank 3.

Last Modified on 28/Feb/06 by jon.mccammond(at)math.ucsb.edu.