Back close

Course Detail

Course Name Homological Algebra
Program M.Phil. in Mathematics (Offered at Kochi Campus)
Year Taught 2019
Degree Postgraduate (PG)
School School of Arts and Sciences
Campus Kochi


Unit 1: Simplical Complexes and Homology Groups

Definition and elementary properties-Siplices, Simplical complexes and Simplical maps, homology Groups, Zero-dimensional Homology, The Homology of a cone, Homomorphism induced by Simpicial Maps, Chain Complexes and Acyclic Carriers.

Unit 2: Relative Homology and Eilenberg-Steenrod Axioms

Relative Homology, the Exact Homology Sequence, the Zig-zag Lemma, Mayer-Vietoris Sequences, the Eilenberg-Steenrod Axioms, the Axioms for Simplicial Theory. Categories and functors.

Unit 3: Singular Homology

The Singular Homology Groups, the Axioms for Singular Theory, Excision in Singular Homology, Mayer-Vietoris Sequences, the Isomorphism between Simplical and Singular Homology, More on Quotient Spaces, CW Complexes and their Homology.

Unit 4: Cohomology and Homological Algebra​​​​​​​

The Hom functor, Simplical Cohomology Groups, Relative Cohomology, Cohomology theory, The Ext Functor, The Universal Coefficient Theorem for Cohomology, Torsion Products, The Universal Coefficient Theorem for Homology, Kunneth Theorems (for cohomology and homology proofs can be omitted).

Unit 5: Applications​​​​​​​

Local Homology Groups and Manifolds, the Jordan Curve Theorem, Projective spaces and Lens Spaces, The Cohomology Ring of a Product Space.


  1. Algebraic Topology, Tammo tom Dieck, European Mathematical Society (2008).
  2. Algebraic Topology, C.R.F.Maunder, Cambridge University Press, (1980).

DISCLAIMER: The appearance of external links on this web site does not constitute endorsement by the School of Biotechnology/Amrita Vishwa Vidyapeetham or the information, products or services contained therein. For other than authorized activities, the Amrita Vishwa Vidyapeetham does not exercise any editorial control over the information you may find at these locations. These links are provided consistent with the stated purpose of this web site.

Admissions Apply Now