Why is it interesting to laminate a genus-2 surface?

Why is it interesting to laminate a genus-2 surface?

We are interested to understand the structure of a group G (is it abelian, or a product of abelian groups, or a free group of some kind etc.). In general, this is a (very) hard question. One strategy is to let G act on some well known (topological) space. Often by...
A rejoinder to the ‘Discovery’

A rejoinder to the ‘Discovery’

Nehru writes, ‘very little original work on mathematics was done in India after the twelfth century till we reach the modern age. ‘Discovery of India’ was written over five months when Nehru was imprisoned in the Ahmednagar Fort. It was first...
Adventures in Geometry 1

Adventures in Geometry 1

Teacher: Stationary objects such as triangles, points or circles are not that interesting in their own right. Instead, we will explore motion. Fix a point O on a piece of paper. Pick any point A. Draw an arrow from O to A. Now begin pushing the arrow OA (keeping A...
After all, functors are well known! 

After all, functors are well known! 

After all, functors are well known! When you convert an object into another kind, surely functions in-between those objects also transform into a new breed. Let’s look at one example: Objects: Topological Spaces (X) Functions between Objects: Continuous maps (f)...
A familiar Functional Equation

A familiar Functional Equation

Cauchy’s functional equations are very simple. The most familiar one has a simple formula: f(x + y) = f(x) + f(y) But first, for the uninitiated, what is a functional equation after all?  What is a functional equation? Usually, functions appear as formulae. For...