MA40040: Algebraic topology
[Page last updated: 03 August 2022]
Academic Year:  2022/23 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Masters UG & PG (FHEQ level 7) 
Period: 

Assessment Summary:  EX 100% 
Assessment Detail: 

Supplementary Assessment: 

Requisites:  Before taking this module you must take MA10209 AND take MA10210 AND take MA30055 
Learning Outcomes:  At the end of the course, the students will be conversant with the basic ideas of homotopy theory and, in particular, will be able to compute the fundamental group of several topological spaces. 
Aims:  The course will provide a solid introduction to one of the Big Machines of modern mathematics which is also a major topic of current research. In particular, this course provides the necessary prerequisites for postgraduate study of Algebraic Topology. 
Content:  Topics will be chosen from the following:
Paths, homotopy and the fundamental group. Homotopy of maps; homotopy equivalence and deformation retracts. Computation of the fundamental group and applications: Fundamental Theorem of Algebra; Brouwer Fixed Point Theorem.
Covering spaces. Pathlifting and homotopy lifting properties. Deck translations and the fundamental group. Universal covers.
Loop spaces and their topology. Inductive definition of higher homotopy groups. Long exact sequence in homotopy for fibrations.

Programme availability: 
MA40040 is Optional on the following programmes:Department of Computer Science

Notes:
