The minimal projective bimodule resolutions of the exterior algebras are explicitly constructed. They are applied to calculate the Hochschild (co)homology of the exterior algebras. Thus the cyclic homology of the exterior algebras can be calculated in case the underlying field is of characteristic zero. Moreover, the Hochschild cohomology rings of the exterior algebras are determined by generat...

We prove that an integral homology 3–sphere is S3 if and only if it admits four periodic diffeomorphisms of odd prime orders whose space of orbits is S3 . As an application we show that an irreducible integral homology sphere which is not S3 is the cyclic branched cover of odd prime order of at most four knots in S3 . A result on the structure of finite groups of odd order acting on integral ho...

The minimal projective bimodule resolutions of the exterior algebras are explicitly constructed. They are applied to calculate the Hochschild (co)homology of the exterior algebras. Thus the cyclic homology of the exterior algebras can be calculated in case the underlying field is of characteristic zero. Moreover, the Hochschild cohomology rings of the exterior algebras are determined by generat...

Symmetric homology of a unital algebra A over a commutative ground ring k has been defined using derived functors and the symmetric bar construction of Fiedorowicz, in an analogous way as cyclic, dihedral or quaternionic homology has been defined. In this paper, it is found that the HS∗(A) admits Dyer-Lashoff homology operations, and indeed, there is a Pontryagin product structure making HS∗(A)...