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pivoxa15
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I am looking for the most basic but rigorous to some extent book on Algebraic topology out there.
Chris Hillman said:Greenberg and Harper has the virtue of not using too many words
I think Hatcher's beautiful book is an important addition to the roster, but probably that it is intended for students who aren't feeling overwhelmed.
It's not!Algebraic topology for dummies?
i also recommend massey's book on differential topology, first steps.
Algebraic topology is a branch of mathematics that deals with the study of topological spaces using algebraic tools. It is important because it allows us to classify and understand the properties of spaces by assigning algebraic structures to them.
Some of the basic concepts and techniques used in algebraic topology include homotopy, homology, cohomology, and fundamental groups. These tools help us to understand the properties of topological spaces and their invariants.
Algebraic topology differs from other branches of topology in that it uses algebraic techniques to study topological spaces, whereas other branches may use geometric or analytical methods. This allows for a more rigorous and systematic approach to understanding topological spaces.
Algebraic topology has applications in various fields such as physics, computer science, and engineering. It is used to study and model complex networks, analyze data and patterns, and solve optimization problems.
Yes, anyone can learn algebraic topology with dedication and practice. It is a complex branch of mathematics, but with patience and perseverance, anyone can understand its concepts and techniques.