Exotic affine space
Okay, imagine you have a very big room with nothing in it. You can call this room the "space" you're in. Now, imagine that you have a piece of paper with a picture of a city on it. There are streets, buildings, and people walking around. This picture is called a "plane", because it's flat and you can't move up or down in it. You can only move left or right, or up or down.
Now, take that piece of paper and hold it up in the big room. The paper isn't part of the room, but it's still there. You can move around the room and look at the paper from different angles, but you can't go into the paper or touch any of the things in the city. This is kind of like an "exotic affine space".
An exotic affine space is a way of thinking about shapes and spaces that aren't like the flat, regular shapes we are used to. Just like how the picture of the city is a different kind of space than the big room it's in, exotic affine spaces are different kinds of spaces that can be put "on top of" other spaces we already know about.
So, when we talk about exotic affine spaces, we're talking about ways of thinking about shapes and spaces that are different from what we're used to, and that can be put on top of other spaces to create new and interesting shapes and patterns. It's kind of like how you can make a city out of a piece of paper, even though it's not really there.
Now, take that piece of paper and hold it up in the big room. The paper isn't part of the room, but it's still there. You can move around the room and look at the paper from different angles, but you can't go into the paper or touch any of the things in the city. This is kind of like an "exotic affine space".
An exotic affine space is a way of thinking about shapes and spaces that aren't like the flat, regular shapes we are used to. Just like how the picture of the city is a different kind of space than the big room it's in, exotic affine spaces are different kinds of spaces that can be put "on top of" other spaces we already know about.
So, when we talk about exotic affine spaces, we're talking about ways of thinking about shapes and spaces that are different from what we're used to, and that can be put on top of other spaces to create new and interesting shapes and patterns. It's kind of like how you can make a city out of a piece of paper, even though it's not really there.