# 미분다양체론

# (微分多樣體論, Differentiable Manifolds)

교과목 번호: 3341.505 (3-3-0)

## Prerequisites

- Linear Algebra
- Basic ODE
- Advanced Calculus (Inverse Function Theorem, Implicit Function Theorem)
- General Topology

## Syllabus

Week 1: Topological Manifolds
Week 2: Smooth Structures and Smooth Manifolds
Week 3: Smooth Maps and Submanifolds
Week 4: Lie Groups
Week 5: Tangent Vectors and Cotangent Vectors
Week 6: Riemannian Manifolds
Week 7: Midterm
Week 8: Vector Fields and Flows
Week 9: Vector Bundles
Week 10: Tensors
Week 11: Differential Forms
Week 12: Cohomology
Week 13: Integration
Week 14: Classification
Week 15: Final Exam

## References

John M. Lee, * Introduction to Smooth Manifolds*, 2nd ed., Springer-Verlag, 2013.

M. Spivak, *A Comprehensive Introduction to DIFFERENTIAL GEOMETRY*, Vol.
I, 3rd ed., Publish or Perish, 1999.

### Easier References

M. Spivak, * Calculus on Manifolds*, 1965.

L. W. Tu, *An Introduction to Manifolds*, 2nd ed., Springer, 2011.

### Advanced References

Jeffrey M. Lee, * Manifolds and Differential Geometry*, Amer. Math. Soc., 2009.

C. H. Taubes, *Differential Geometry*, Oxford Univ. Press, 2011.

R. W. Sharpe, *Differential Geometry*, Springer, 1996.