Topological group cohomology with loop contractible coefficients

The Cohomology of a Coxeter Group with Group Ring Coefficients

Topological Gauge Theories and Group Cohomology

We show that three dimensional Chern-Simons gauge theories with a compact gauge group G (not necessarily connected or simply connected) can be classified by the integer cohomology group H(BG,Z). In a similar way, possible Wess-Zumino interactions of such a group G are classified by H(G, Z). The relation between three dimensional Chern-Simons gauge theory and two dimensional sigma models involve...

Cohomology of topological groups with applications to the Weil group

We establish various properties of the definition of cohomology of topological groups given by Grothendieck, Artin and Verdier in SGA4, including a Hochschild-Serre spectral sequence and a continuity theorem for compact groups. We use these properties to compute the cohomology of the Weil group of a totally imaginary field, and of the Weil-étale topology of a number ring recently introduced by ...

Floer Cohomology and Non - Contractible Periodic Orbits

For a closed symplectic manifold (M,ω), a compatible almost complex structure J , a 1-periodic time dependent symplectic vector field Z and a homotopy class of closed curves γ we define a Floer complex based on 1-periodic trajectories of Z in the homotopy class γ. We show how to associate to the above data an invariant, the symplectic torsion, which is an element in the Whitehead group Wh(Λ0), ...

Cohomology with Chains as Coefficients

THE cohomology theory described in the title is obtained by replacing the usual coefficient group by an arbitrary chain complex. This theory satisfies all of the Eilenberg-Steenrod axioms for a cohomology theory except the dimension axiom. There are other theories with this property, and among these our theory is probably the least extraordinary. That is to say, its definition and techniques ar...