Cohomotopy group
Dear little one, do you know what a circle is? It's a simple shape that just goes round and round. Now imagine a rubber band wrapped around a sphere. If you stretch and twist the rubber band, you can make all sorts of different loops on the sphere. These loops are like the circles you know, but they are "bendy" and can be stretched or squished.
Cohomotopy group is a way of understanding and classifying these loops on a sphere, or on any other shape for that matter. It's like putting loops into different groups based on how similar they are to each other.
To do this, we use something called a cohomology theory, which is kind of like a special set of rules that we follow to classify the different loops. This cohomology theory works by assigning numbers to the loops based on certain properties they have.
Now imagine a bunch of people trying to describe their favorite path on this sphere. They might have different ways of describing it, but using cohomotopy group, we can group together paths that are "the same" even if they are described differently.
So in summary, cohomotopy group is a way of organizing and grouping together different types of loops on a shape by assigning them numbers based on certain properties they have. It helps us understand how similar or different these loops are to each other even if they look different or are described differently.
Cohomotopy group is a way of understanding and classifying these loops on a sphere, or on any other shape for that matter. It's like putting loops into different groups based on how similar they are to each other.
To do this, we use something called a cohomology theory, which is kind of like a special set of rules that we follow to classify the different loops. This cohomology theory works by assigning numbers to the loops based on certain properties they have.
Now imagine a bunch of people trying to describe their favorite path on this sphere. They might have different ways of describing it, but using cohomotopy group, we can group together paths that are "the same" even if they are described differently.
So in summary, cohomotopy group is a way of organizing and grouping together different types of loops on a shape by assigning them numbers based on certain properties they have. It helps us understand how similar or different these loops are to each other even if they look different or are described differently.