# Algebraic topology III Seminar, Fall/Winter 2011

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Coordinator: Fan Honglu (樊宏路)

Email: lethe DOT ar AT gmail DOT com

Mobile: 136 4571 8458 (680458)

Textbook: Differential Forms in Algebraic Topology

## Schedule: Sep. 17, 2011 - Jan. 5, 2012 Saturday Mornings, 9:00 am - 12:00 am, Center of Mathematical Sciences Building 316

09.17. The de Rham complex on \mathbb R^n; The Mayer-Vietoris sequence; Orientation and integration; Poincaré Lemmas, speaker: Fan Honglu (樊宏路)

09.24. The Mayer-Vietoris argument, speaker: Zeng Mingcong (曾鸣聪)

10.08. The Thom isomorphism, speaker: Xu Chao (许超)

10.15. The nonorientable case, speaker: Xie Fei (谢斐)

10.22. The generalized Mayer-Vietoris principle; More examples and applications; Presheaves and Cech cohomology, speaker Fan Honglu (樊宏路)

11.5. Sphere bundles - first half, speaker: Zhao Huijun (赵慧君)

11.19. Sphere bundles - second half, speaker:

11.26. The Thom isomorphism and poincaré duality revisited, speaker:

12.3. Monodromy, speaker:

12.10. Chern classes of a complex vector bundle, speaker:

12.17. The splitting priniple and flag manifolds

12.24. Pontrjagin classes

12.31. The search fo the universal bundle

1.7. Spectral sequences

## Introduction

This is a continuation of Algebraic topology I & II in previous semesters. But the prerequisites are actually low. Although algebraic topology is not exactly what this book covers, the materials is still a good complement for what we learned before. Whether to talk about spectral sequences is up to the speed of this seminar.
We will cover Chapters 1,2 and 4, and finally talk about spectral sequence as much as we can.

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