Introduction to Algebraic Topology
Deep Kundu, Daniel Sukumar · Research Archive of Indian Institute of Technology Hyderabad (Indian Institute of Technology Hyderabad) · 2017
In this report we discuss the basic concepts and the need of studying Algebraic Topology. We cover the idea of fundamental groups in detail and use it to prove some important results like the Brouwer’s Fixed point theorem. Finally we set our- selves up for a major result of this field namely The Seifert Van Kampen Theorem. In the next part of the thesis we discuss about the homology groups which over- comes some the shortcomings of the fundamental groups, specifically distinguish- ing between higher dimensional surfaces.