In general, the material on the exam is everything we covered in the course but does not include the TDA material we did at the end. So it does not include functors and pushouts, simplicial complexes and homology and the VR and Reeb complexes

These  homeworks, review problems and exams will give you some idea of the kind of problems to expect. The problems on TDA which are not on the exam are crossed off in the relevant documents.

• tophw2.1
• tophw2.2
• tophw2.3
• tophw2.4
• tophw2.5
• toprev2.1
• toprev2.2
• topexam2.1
• topexam2.2

Here is the material covered, Numbers in parentheses are section number from Munkres, Topology, 2nd edition. Some sections had just partly covered.

• Path homotopy (51)
• Fundamental group (52)
• Covering spaces (introduction) (53)
• Fundamental group of the circle (54)
• Retractions and fixed points (55)
• Borsuk-Ulam Theorem (57)
• Deformation retract and homotopy (58)
• Fundamental group of spheres (59)
• Fundamental group of sme surfaces
• Identification spaces and quotient topology (22)
• Algebraic preliminaries to SVK theorem (67-69)
• The SVK- push out, classical and generator/relation versions (70)
• Fundamental group of wedge of circles, the torus, the dunce cap, the projective plane (71, 73, 74)
• Abelianization of fundamental group (first Homology) (75)
• Embeddings of manifolds (36)
• Tychonoff Theorem (37)
• Stone-Čech compactification (38)