Gysin sequence

Imagine you have a set of building blocks that you want to stack up. You start with one block at the bottom, then you add another block on top of it. Now you have two blocks stacked. You can keep adding blocks on top of each other to make a really tall tower.

The gysin sequence is a lot like building a tower with blocks, but instead of blocks we use something called vector bundles. Vector bundles are like bundles of arrows, and they help us understand how spaces twist and turn in different directions.

To build the gysin sequence, we start with a curved space, like a hill or a valley. We can think of this space as our first block. Then we add a vector bundle on top of the space, which is like adding another block to our tower.

Next we add another vector bundle on top of the first one, and this is like adding a third block to our tower. We keep adding more vector bundles on top of each other, each one representing a new twist or turn in our space.

The gysin sequence helps us understand how these different twists and turns affect things like integrals or cohomology, which are ways of measuring how much "stuff" there is in a space.

So, just like building a tower with blocks, we can build a gysin sequence with vector bundles to help us understand how spaces twist and turn.