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1MA259 Differential Topology, Spring 2017

Dually, a topological semimetal can be represented by Euler chains from which its surface Fermi arc connectivity can be deduced. These dual pictures, and the link to topological invariants of insulators, are organised using geometric exact sequences.

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We go beyond Dirac-type Hamiltonians and introduce new classes of semimetals whose local charges are subtle Atiyah—Dupont—Thomas invariants globally constrained by the Kervaire semicharacteristic, leading to the prediction of torsion Fermi arcs. Abstract arXiv The subtle interplay between local and global charges for topological semimetals exactly parallels that for singular vector fields.

M4P54 - Differential Topology | Faculty of Engineering | Imperial College London

The first part of the course of the course will be concerned with de Rham cohomology, which is a relatively approachable form of cohomology for smooth manifolds. Time permitting, we will then look at singular homology and cohomology, the relation between singular and de Rham cohomology via the de Rham theorem, and Morse theory.

It is expected that you will have taken the courses Algebraic Topology M3P21 and Manifolds M4P52 , or have learnt the relevant material elsewhere. In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:.

Knotted surfaces in 4-manifolds and their surgeries

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About this subject Overview Eligibility and requirements Assessment Dates and times Further information Timetable opens in new window Single page view for printing Contact information Please refer to the specific study period for contact information.