Mathematics 205ABC Qualifying Examination Fall 2011 This summarizes the material for the examination In addition to the references from the official text Bredon Topology and Geometry there are also alternate more detailed references often with numerous exercises that are strongly recommended especially for the third course in the sequence Syllabi for the first and third courses are given in the following online files http math ucr edu wlgan math205A html http math ucr edu res math205C 2011 outline205C pdf Mathematics 205A Coverage in Bredon Chapter I except for Section 6 Alternate references Munkres Topology 2000 Edition Chapters 2 3 except the supplementary exercises 4 except Section 36 5 6 8 9 only Sections 51 and 59 Hatcher Algebraic Topology Chapter 0 except for the subsections on cell complexes and the Homotopy Extension Property Several files in the online directory http math ucr edu res math205A may also be useful The same applies to the discussion of Munkres Section 51 in the following online file http math ucr edu res math205B math205Bcommentaries pdf Mathematics 205B Coverage in Bredon Chapter II Sections 1 11 Chapter III Sections 1 4 Alternate references Munkres Topology 2000 Edition Chapter 9 Sections 51 54 Chapter 13 Section 79 Hatcher Algebraic Topology Chapter 0 except for the subsections on cell complexes and the Homotopy Extension Property Chapter 1 Sections 1 1 1 3 Lee Introduction to Smooth Manifolds Chapters 1 4 7 8 and 10 Boothby An Introduction to Differentiable Manifolds and Riemannian Geometry close to the preceding reference in many respects but probably less comprehensive Chapters I and II Chapter III Sections III 1 III 5 Chapter IV Sections IV 1 IV 5 Milnor Topology from the Differentiable Viewpoint covers some material not in either of the preceding two references Sections 1 3 Mathematics 205C Coverage in Bredon Chapter III Sections 5 9 Chapter IV Sections 1 10 13 15 17 19 and 21 Alternate references Munkres Topology 2000 Edition Chapter 9 Sections 58 59 Chapter 10 Sections 53 54 only for the results on planar and nonplanar graphs somewhat different proofs for these results were given in the course Chapter 11 Sections 63 64 Chapter 13 Sections 79 81 Chapter 14 Sections 84 85 Hatcher Algebraic Topology Chapter 0 Chapter 1 Sections 1 2 1 3 Chapter 2 Sections 2 1 2 3 2 A 2 B except for the explicit construction of singular homology in Section 2 1 The following directory contains notes from the course as it was taught in the Spring 2011 Quarter along with various related files Studying the files in this directory is very strongly recommended however the material in the files computingHq pdf and cell euler pdf was not covered in the course and will not be covered in the examination http math ucr edu res math205C 2011 Note that this is NOT the same as http math ucr edu res math205C which contains material similar to that of 205B as it was taught during the Winter 2011 Quarter but is not on the recommended list Several files in the online directory http math ucr edu res math205B may also be useful In particular the file http math ucr edu res math205B math205Bcommentaries pdf contains additional discussions of certain sections in Munkres and the portions dealing with Sections 51 54 59 63 64 to the bottom of page 30 67 71 and 79 85 up to the end of the proof in the middle of page 54 are recommended there are also three supplementary commentary files with additional material Other files from that directory which may be useful include the files with exercises and solutions as well as the following http math ucr edu res math205B categories pdf background on category theory http math ucr edu res math205B lifting pdf http math ucr edu res math205B examples pdf http math ucr edu res math205B ahlfors pdf up to the eighth line from the bottom