Math 601A: Topics in Topology - Orbifolds

Fall 2007

MW 4:40-6:10pm in LN 2205

Hi all. This is a very basic page that will be under construction throughout the semester. It will contain references for the material we cover as well as a copy of the most up to date online notes. Remember that you are responsible for keeping the notes up to date.

References for Transformation Groups: Here is an incomplete list of possible references for transformation group theory (equivariant topology)

Transformation Groups, by Tammo tom Dieck, De Gruyter Studies in Mathematics 8.
Seminar on Transformation Groups, by Armand Borel
Transformation Groups and Algebraic K-theory (mainly the first chapter), by Wolfgang Lück.

You may notice that Lück's book has a hyperlink. That's because Wolfgang Lück has all of his publications availible for free on his webpage. This includes scanned copies of his books. If you click on the link, you will be taken to his publication list where you can download his book. Part(i) is the part to look at for the foundations of transformation groups. It is a large file, so keep that in mind.

References for Bredon Cohomology and Equivariant Cohomology:

Equivariant Cohomological Chern Characters by Wolfgang Lück.
Equivariant Cohomology Theories by Glen Bredon. This is a short note from 1966 about his construction of equivariant cohomology, not a detailed description.

References for Orbifolds: Here is a list of a few papers about topics on orbifolds. All of them are availible for free online.

Orbifolds as Groupoids: an introduction by Ieke Moerdijk from 2002.
A New Cohomology Theory for Orbifold by Weimin Chen and Yongbin Ruan from 2000.

Other papers will be added as the semester progresses.

Another reference that you can use for orbifolds is the book Orbifolds and Stringy Topology by Alejandro Adem, Yongbin Ruan, and Johann Leida. It is number 171 in the Cambridge Tracts in Mathematics series published June 2007. There is a copy in the library, and I have a copy which I will be happy to loan out for a short time on request.

Class Notes: Here are the notes last updated 10/2/2007. There are undoubtedly typos. Also, I tried to put a little more into them than I did in class. Remember that you guys will be taking turn typing up the notes throughout the semester.

Notes

Also, here are some papers concerning geometric realization of semi-simplicial sets, nerves of categories, and classifying spaces of categories.

The Geometric Realisation of a Semi Simplicial Complex by John Milnor from 1957.
Classifying spaces and spectral sequences by Graeme Segal from 1968.

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Binghamton University Mathematical Sciences Department