Time/venue: Thursday 10:15-12:00, Max Planck Institute for Mathematics, seminar room
Sheaves and cohomology are ubiquitous in geometry and topology. The derived category of sheaves on a space, together with the so-called "six functors" (and the various relations between them), form an "enhancement" of the cohomology groups of spaces that provides more insight into the structure behind these cohomology groups (see e.g. [A1]).
Equivariant cohomology is a cohomology theory for G-spaces (spaces equipped with a group action), that remembers much more about the G-space than just the singular cohomology of its orbit space (rather, it should be thought of as cohomology of the "quotient stack"). In the book Equivariant sheaves and functors [1], Bernstein and Lunts construct a generalization of the aforementioned derived category and six functors for G-spaces, that forms an "enhancement" of equivariant cohomology.
The aim of this reading seminar will be to get to understand parts I and II of this book, with as our end-goal Theorem 12.7.2. Before turning to this book, we will spend some time to first learn about the more classical story for sheaves on spaces (without a group action).
Some knowledge about abelian categories will probably be assumed. A basic knowledge of Lie groups is also useful.
The seminar will have weekly talks of 1:00-1:30 hours.
The dates of the session are subject to changes and not strict since some topics may take more time than an entire meeting and some less.
Textbooks
[1] J. Bernstein and V. Lunts, Equivariant sheaves and functors, Springer-Verlag 1994.
[2] A. Borel et al. , Intersection cohomology, Birkhauser 1984.
[3] B. Iversen, Cohomology of sheaves, Springer-Verlag 1986.
[4] C.A. Weibel, An introduction to homological algebra, Cambridge University Press 1994.
Additional literature
[A1] Martin Gallauer, https://homepages.warwick.ac.uk/staff/Martin.Gallauer/docs/m6ff.pdf [3]
More to be added along the way.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/41
[2] https://www.mpim-bonn.mpg.de/de/node/4234
[3] https://homepages.warwick.ac.uk/staff/Martin.Gallauer/docs/m6ff.pdf