Cohomology Structure of Fixed Point Sets

In June 2024, I gave a talk at the final presentation session for the course Algebraic Topology II by Prof. Seonhee Lim. I introduced the relationship between the cohomology structures of a space and that of the fixed point set of a $\ZZ_p$ or $S^1$-action on the space. In particular, I covered the Borel construction, the Leray–Hirsch theorem, and the inheritance of the Poincaré duality property. The talk was based on Sections VII.1 and VII.6 of Bredon’s textbook [1].

Slides

These are the slides (with notes) for my talk.

References

[1] Bredon, G. E., Introduction to Compact Transformation Groups. Academic Press, 1972.

[2] Hatcher, A., Algebraic Topology. Cambridge University Press, 2001.

[3] Weibel, C. A., An Introduction to Homological Algebra. Cambridge University Press, 1995.