I was excited to receive a package from the American Mathematical Society today! My author’s copies of “Winding Around” have arrived!
This is a book based on by MASS 2013 course of the same title, which looks at the winding number – the central notion in plane topology – from a variety of perspectives, topological, geometrical, analytic and combinatorial. Having (I hope) made the case that the winding number concept is the “golden cord which guides the student through the labyrinth of classical mathematics”, I conclude by following a beautiful paper of Michael Atiyah to explain how, by asking one natural question about the winding number, we can be led to the Bott periodicity theorem, a central result in the flowering of topology in the 1960s.
If you are interested in the book, please visit the AMS bookstore page.
I will attempt to maintain a list of typos and other corrections here. At present this list is empty, but I doubt if that happy state of affairs will last for long! (edit: it didn’t) Please contact me with any information about corrections. And, to quote the final sentence of the book, “I wish you much happy winding around in the future.”