Date 
Topics 
References 
Week 1 
Jan 09 
Historical motivation and applications. 
 Cohomology of groups, by K.S. Brown. (Introduction)
 Der Cohomologie Ring einer beliebigen Gruppe, by B. Eckmann.
 Relations between homology and homotopy groups I, II, by S. Eilenberg and S. MacLane.
 Der Einfluss der Fundamentalgruppe auf die Bettischen Gruppen, by H. Freudental.
 Fundamentalgruppe und zweite Bettische Gruppe, by H. Hopf.
 Selecta Heinz Hopf, by H. Hopf.
 Über die Bettische Gruppen, die zu einer beliebige Gruppe gehören, by H. Hopf.

Jan 10 


Jan 11 
Group homology from the point of view of homological algebra. 
Cohomology of groups, by K.S. Brown. (I.03, I.78, II.13, III.01) 
Jan 12 


Jan 13 
The relationship between group (co)homology and the functors Tor, Ext. 
Cohomology of groups, by K.S. Brown. (III.02) 
Week 2 
Jan 16 
Martin Luther King Jr. Day. No class today. 

Jan 17 


Jan 18 
The bar resolution and the classifying space. 
 Cohomology of groups, by K.S. Brown (I.5, II.4, II.6, III.6, III.8)
 Cohomology of finite groups, by A. Adem and R.J. Milgram. (II.1, II.3)
 The cohomology of groups, by L. Evens (2.3)
 Representations and cohomology I, by D.J. Benson (3.4)
 Representations and cohomology II, by D.J. Benson (2.12.4)

Jan 19 


Jan 20 
Milnor's construction and the simplicial construction of the classifying space. 
 Cohomology of finite groups, by A. Adem and R.J. Milgram. (II.1)
 Representations and cohomology II, by D.J. Benson (2.32.4)

Week 3 
Jan 23 
No class today. To be rescheduled. 

Jan 24 


Jan 25 
No class today. To be rescheduled. 

Jan 26 


Jan 27 
Functoriality, restriction and transfer maps. 
 Cohomology of groups, by K.S. Brown (III.6, III.8, III.910)
 Cohomology of finite groups, by A. Adem and R.J. Milgram. (II.5)
 The cohomology of groups, by L. Evens (4.1, 4.2)
 Representations and cohomology II, by D.J. Benson (2.7)

Week 4 
Jan 30 


Jan 31 


Feb 01 
Transfer and the primary decomposition 
 Cohomology of groups, by K.S. Brown (III.910)
 Cohomology of finite groups, by A. Adem and R.J. Milgram. (II.5)
 The cohomology of groups, by L. Evens (4.1, 4.2)
 Representations and cohomology II, by D.J. Benson (2.7)

Feb 02 


Feb 03 
Invariants and stable elements 
 Cohomology of groups, by K.S. Brown (III.10)
 Cohomology of finite groups, by A. Adem and R.J. Milgram. (II.6)
 The cohomology of groups, by L. Evens (4.2)

Week 5 
Feb 06 


Feb 07 


Feb 08 
Fibrations and spectral sequences 
 Cohomology of groups, by K.S. Brown. (VII.16)
 A user's guide to spectral sequences, by J. McCleary
 Spectral sequences in algebraic topology, by A. Hatcher (Chapter 1)
 Representations and cohomology II, by D.J. Benson (3.13.5)

Feb 09 


Feb 10 
Spectral sequence computations 
 Cohomology of groups, by K.S. Brown. (VII.16)
 A user's guide to spectral sequences, by J. McCleary
 Spectral sequences in algebraic topology, by A. Hatcher (Chapter 1)
 Representations and cohomology II, by D.J. Benson (3.9)

Week 6 
Feb 13 


Feb 14 


Feb 15 
The second (co)homology group and extensions. 
Cohomology of groups, by K.S. Brown. (I.5, IV.3) 
Feb 16 


Feb 17 
The cohomology of finite categories and higher limits. 
Representations and cohomology of finite categories, by F. Xu. (1.1.3, 3.1) 
Week 7 
Feb 20 
Presidents' day. No class today. 

Feb 21 


Feb 22 
The bar resolution for finite categories. 
Representations and cohomology of finite categories, by F. Xu. (1.2.2, 2, 4.1.2) 
Feb 23 


Feb 24 
Homotopy colimits and obstructions I. 

Week 8 
Feb 27 
Homotopy colimits and obstructions II. 

Feb 28 


Feb 29 
Quillen's solution to the AtiyahSwan conjecture I. 
The spectrum of an equivariant cohomology ring I and II, by D. Quillen. 
Mar 01 


Mar 02 
Quillen's solution to the AtiyahSwan conjecture II. 
The spectrum of an equivariant cohomology ring I and II, by D. Quillen. 
Week 9 
Mar 05 


Mar 06 


Mar 07 
Periodic cohomology and free actions on spheres. 
 Cohomology of finite groups, by A. Adem and R.J. Milgram. (IV.6)
 Groups which act on S^{n} without fixed point, by J. Milnor.

Mar 08 


Mar 09 
Milnor's condition and free actions on homotopy spheres. 
 Groups which act on S^{n} without fixed point, by J. Milnor.
 Cohomology of groups, by K.S. Brown (I.6)
 Periodic resolutions for finite groups, by R.G. Swan.

Week 10 
Mar 12 


Mar 13 


Mar 14 
Periodic resolutions and homotopy spheres. 
 Periodic resolutions for finite groups, by R.G. Swan.
 Induced representations and projective modules, by R.G. Swan.

Mar 15 


Mar 16 
The spherical space form problem and free actions of groups on products of spheres. 
 Periodic resolutions for finite groups, by R.G. Swan.
 Induced representations and projective modules, by R.G. Swan.
 Constructing and deconstructing group actions, by A. Adem.
