Characteristic classes and applications: Fall 2019

Materials

• Sept 7 updated syllabus

• Questionnaire

• L1 notes by Orsola Capovilla-Searle

• L2 Stiefel-Whitney classes, notes by Orsola Capovilla-Searle

• L3 Stiefel-Whitney classes continued, notes by Orsola Capovilla-Searle

• L4 Parallelizable real projective spaces, notes by Orsola Capovilla-Searle

• L5 Grassmannians, notes by Orsola Capovilla-Searle

• L6 Classification of vector bundles, notes by Orsola Capovilla-Searle

• L7 Classification of vector bundles continued, notes by Orsola Capovilla-Searle

• L8 Leray-Hirsch theorem and canonical bundle of Grassmannians, notes by Orsola Capovilla-Searle

• L9 Construction of Chern and Stiefel-Whitney classes, notes by Orsola Capovilla-Searle

• L10 Splitting principle, notes by Orsola Capovilla-Searle

• L11 Cohomology of Grassmannians, notes by Orsola Capovilla-Searle

• L12 Thom spaces, notes by Orsola Capovilla-Searle

• L13 Orientations, notes by Orsola Capovilla-Searle

• L14 Euler class, notes by Orsola Capovilla-Searle

• L15 Thom classes and Poincare Duality, notes by Orsola Capovilla-Searle

• L16 Purity and more on the Euler class, notes by Orsola Capovilla-Searle

• L17 Pontryagin classes, notes by Orsola Capovilla-Searle

• Problem set 1

• Problem set 2

• Problem set 3

• Problem set 4

• Midterm