## Details of MA4206 (Spring 2017)

Level: 4 |
Type: Theory |
Credits: 3.0 |

Course Code | Course Name | Instructor(s) |
---|---|---|

MA4206 |
Algebraic Topology |
Somnath Basu |

Syllabus |
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MA4103 : Algebraic Topology
Homotopy Theory: Homotopy and homotopy equivalence; retraction, deformation retract, contractible spaces; fundamental groups; covering spaces, path lifting and homotopy lifting; fundamental group of S1; Borsuk-Ulam theorem, Van-Kampen theorem; fundamental group of Sn; Brouwers no-retraction and fixed point theorem in dimension two. Homology Theory: Barycentric subdivision; finite simplicial complexes and their geometric realizations; simplicial approximation theorem; triangulable spaces, triangulation of standard manifolds; simplicial chain complex, simplicial homology; computation of simplicial homology groups of Sn, RPn and Klein bottle. |

References |
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Suggested Texts/Reference Books:
1. Massey, W. S., A Basic Course in Algebraic Topology, Springer-Verlag, 1991. 2. Munkres, J. R., Elements of Algebraic Topology, Addison-Wesley, 1984. 3. Spanier, E. H., Algebraic Topology, Springer-Verlag, 1966. |

#### Course Credit Options

Sl. No. | Programme | Semester No | Course Choice |
---|---|---|---|

1 | IP | 2 | Not Allowed |

2 | IP | 4 | Core |

3 | IP | 6 | Not Allowed |

4 | MR | 2 | Not Allowed |

5 | MR | 4 | Not Allowed |

6 | MS | 8 | Core |

7 | RS | 1 | Elective |

8 | RS | 2 | Not Allowed |