MA3H5 : Manifolds

This is the (unofficial) website of MA3H5.


Monday 12am, B3.02.
Thursday 11am, MS.05.
Friday 10am, MS.05.

Support classes with Yiwen Chen. Current plan:
Week 5: Thursday 10am, MS.03.
Week 6: Thursday 10am, B2.04/5 Science Concourse
Week 7: Thursday 10am, MS.03.
Week 8: Thursday 9am, MS.05.
Week 9: Thursday 10am, MS.03.
Week 10: Thursday 10am, B2.04/5 Science Concourse


The course assessment is 100% written examination.
The format of the examination will be: One complulsory question worth 40 marks and a choice of three out of four optional questions worth 20 marks each.


Manifolds in euclidean space, smooth maps, tangent spaces, immersions and submersions, tangent and normal bundles, orientations, abstract manifolds, vector bundles, partitions of unity, differential forms, integration, Stokes's theorem.

Official page

The course also has an Offical web page.

Course notes

Course notes
Note: These are have only recently been prepared. Almost certainly there are still some mistakes in them. I will post any significant corrections as they are noticed.


Sheet 1
Sheet 2
Sheet 3
Sheet 4
Sheet 5
Sheet 6

Other notes

Course notes for MA455 Manifolds by David Mond.

Prior to 2014, a course with the same title was given as a 4th-year module. The course notes above give a nice account of much of the material in the current 3rd year unit. Lots of pictures, more examples and explanations. I have used it in preparing my own notes. It covers most (but not all) of the current course, and lots more. (There is a lot of stuff about transversality which is not in the present course. Conversely, I was planning to say something about general vector bundles, which is not discussed in these notes.)


Sphere eversions: turning a sphere inside out through immersions: Scary video: Optiverse video and explanations: Optiverse page

Mechanical linkages: manifolds as configuration spaces: WP page, and a paper by (our very own) Magalhaes and Pollicott here, with reference to the Thurston-Weeks Linkage (surface of genus 2).


L. W. Tu, ``An Introduction to Manifolds'', Universitext Springer-Verlag (2010). QA613.T8.
[Covers most of the material in the course fairly efficiently.]

J. M. Lee, ``Introduction to Smooth Manifolds'', Graduate Texts in Mathematics, Springer (2013). QA613.L3.
[Good introductory text. Develops the theory from basic material to more advanced topics. Covers most of the course. 600+ pages.]

F. Warner, ``Foundations of differentiable manifolds and Lie groups'', Graduate Texts in Mathematics, Springer (2010). QA614.3.W2.
[A more formal treatment. Progresses quite quite quicky on to more advanced topics.]

W. Boothby, ``An introduction to differentiable manifolds and Riemannian geometry'', Academic Press (2003). QA614.3.B6.