# MA3H5 : Manifolds

This is the (unofficial) website of MA3H5.

### Lectures

Monday 12am, B3.02.

Thursday 11am, MS.05.

Friday 10am, MS.05.
Support classes with Rhiannon Dougall

Starting week 2: Tuesday 4pm, B1.01.

Weeks 3-10: Thursday 10am, MS.03.

### Assessment

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.

### Syllabus

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.

### Exercises

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.)

### Websites

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).

### Books

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.