Mathematics

**MTH 605: Topology I (4)**

*General Topology*: Connectedness, Compactness, Local Compactness, Paracompactness, Quotient Spaces, Topological Groups, and Baire Category Theorem.

*Fundamental Gruops and Covering Spaces*: Homotopy, Homotopy Equivalence and Deformation Retractions, Fundamental Group, Van Kampen Theorem, Deck Transformations, Group Actions, and Classification of covering spaces.

*Cellular and Simplicial Complexes*: Operations on Cell Complexes and Homotopy Extension Property. Simplicial Complexes - Barycentric Subdivision and Simplicial Approximation Theorem.

*Suggested Books*:

- A. Hatcher, Algebraic Topology, Cambridge University Press, 2002.
- J. R. Munkres, Topology, Second Edition, Prentice Hall, 2011.
- G. Bredon, Topology and Geometry, Springer International Edition, 2006.
- W. S. Massey, A Basic Course in Algebraic Topology, Springer International Edition, 2007.
- J. J. Rotman, An Introduction to Algebraic Topology, Springer, 1988.
- J. R. Munkres, Elements of Algebraic Topology, Westview Press, 1996.

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