Is there a class library for spatial operation?

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C#5.0

Hello, I have been doing a small program on winforms working on maps and converting the maps into objects like polygons, poly lines, points.
The thing I want is a class that computes certain spatial or mathematical operations like the followings.
1. do the 2 of the polygons collide?
2. do the 2 poly-lines intersect? or intersect with the above polygons?
3. does the polygon cover another polygon?
etc

ARCGIS already does all of that but I was wandering if there is a class I can include that does all the operations and returns the results.