MATH 7570 Topics in Topology: Equivariant Cohomology Florian Frick Syllabus Lectures: Tue and Thu, 10:10 – 11:25, Malott 206 Instructor: Florian Frick, [email protected], Malott 588 Office hours Wed 2 – 3, Thu 11:30 – 12:30, and by appointment Content The following is a non-exhaustive list of topics: • • • • • An intuitive view of (equivariant) homology and cohomology Borel construction and Serre spectral sequence Fixed points versus homotopy fixed points, Sullivan’s conjecture, localization Fadell–Husseini index theory Applications in combinatorics and discrete geometry Textbooks We will not follow any specific textbook. Some books that I might use to prepare include • Christopher Allday and Volker Puppe, Cohomological Methods in Transformation Groups, Cambridge studies in advanced mathematics 32, Cambridge University Press. • Glen E. Bredon, Introduction to Compact Transformation Groups, Elsevier. • Kenneth S. Brown, Cohomology of Groups, Graduate Texts in Mathematics 87, Springer. • Tammo tom Dieck, Transformation Groups, De Gruyter. • Wu Yi Hsiang, Cohomology Theory of Topological Transformation Groups, Ergebnisse der Mathematik und ihrer Grenzgebiete 85, Springer. • Robert MacPherson, Equivariant Invariants and Linear Geometry, in Geometric Combinatorics, Editors: Ezra Miller, Victor Reiner, Bernd Sturmfels, IAS/Park City Mathematics Series vol. 13, American Mathematical Society. • J. Peter May et al., Equivariant Homotopy and Cohomology Theory, CBMS Regional Conference Series in Mathematics 91, American Mathematical Society. We will additionally cover topics that have not been digested into a textbook treatment. I will point out the appropriate resources to you during the lecture.
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