Whitney sum

The Whitney sum is a mathematical concept that helps us add together two different sets of numbers. Imagine you have two groups of apples, one group has 3 apples and another group has 5 apples. To find out how many apples you have in total, you can use the Whitney sum by first counting how many apples are in the first group (3), and then counting how many apples are in the second group (5). Then you would add these two numbers together (3 + 5) to get the total number of apples (8).

But the Whitney sum isn't just for adding numbers together. It's also used to add together two different mathematical objects called "chains". Chains are sequences of mathematical objects that are connected by "boundaries". These boundaries help us understand how the objects in the chain are related to each other.

To find the Whitney sum of two chains, we start by looking at the first object in each chain and add them together. Then we move on to the second objects in each chain and add them together, and so on, until we have added all the objects in both chains.

For example, imagine we have two chains of shapes. One chain has a triangle and a pentagon, and the other chain has a square and a hexagon. To find the Whitney sum of these two chains, we would start by adding the triangle and square together (which gives us a new shape called a "tri-square"). Then we would add the pentagon and hexagon together (which gives us a new shape called a "pent-hex"). So the Whitney sum of these two chains is the chain that has the tri-square and pent-hex shapes.

Overall, the Whitney sum is a helpful tool for combining and understanding different mathematical objects.