Summary: EQUIVARIANT COHOMOLOGY IN ALGEBRAIC
APPENDIX A: ALGEBRAIC TOPOLOGY
NOTES BY DAVE ANDERSON
In this appendix, we collect some basic facts from algebraic topology
pertaining to the fundamental class of an algebraic variety, and Gysin push-
forward maps in cohomology. Much of this material can be found in [Ful97,
Appendix B], and we often refer there for proofs.
This appendix is in rough form, and will probably change significantly.
(Watch the version date.)
1. A brief review of singular (co)homology
Let X be any space, let CX be the complex of singular chains on X, and
let CX = Hom(CX, Z) be the complex of singular cochains. The singular
homology modules are defined as
HiX = hi(CX),
and the singular cohomology modules are
X = hi