On the transfer reducibility of certain Farrell-Hsiang groups

We show how the existing proof of the Farrell-Jones Conjecture for virtually poly-$\mathbb{Z}$-groups can be improved to rely only on the usual inheritance properties in combination with transfer reducibility as a sufficient criterion for the validity of the conjecture.Comment: 18 page

The gauge structure of generalised diffeomorphisms

We investigate the generalised diffeomorphisms in M-theory, which are gauge transformations unifying diffeomorphisms and tensor gauge transformations. After giving an En(n)-covariant description of the gauge transformations and their commutators, we show that the gauge algebra is infinitely reducible, i.e., the tower of ghosts for ghosts is infinite. The Jacobiator of generalised diffeomorphisms gives such a reducibility transformation. We give a concrete description of the ghost structure, and demonstrate that the infinite sums give the correct (regularised) number of degrees of freedom. The ghost towers belong to the sequences of rep- resentations previously observed appearing in tensor hierarchies and Borcherds algebras. All calculations rely on the section condition, which we reformulate as a linear condition on the cotangent directions. The analysis holds for n < 8. At n = 8, where the dual gravity field becomes relevant, the natural guess for the gauge parameter and its reducibility still yields the correct counting of gauge parameters.Comment: 24 pp., plain tex, 1 figure. v2: minor changes, including a few added ref

Quantization of Even-Dimensional Actions of Chern-Simons Form with Infinite Reducibility

We investigate the quantization of even-dimensional topological actions of Chern-Simons form which were proposed previously. We quantize the actions by Lagrangian and Hamiltonian formulations {\`a} la Batalin, Fradkin and Vilkovisky. The models turn out to be infinitely reducible and thus we need infinite number of ghosts and antighosts. The minimal actions of Lagrangian formulation which satisfy the master equation of Batalin and Vilkovisky have the same Chern-Simons form as the starting classical actions. In the Hamiltonian formulation we have used the formulation of cohomological perturbation and explicitly shown that the gauge-fixed actions of both formulations coincide even though the classical action breaks Dirac's regularity condition. We find an interesting relation that the BRST charge of Hamiltonian formulation is the odd-dimensional fermionic counterpart of the topological action of Chern-Simons form. Although the quantization of two dimensional models which include both bosonic and fermionic gauge fields are investigated in detail, it is straightforward to extend the quantization into arbitrary even dimensions. This completes the quantization of previously proposed topological gravities in two and four dimensions.Comment: 50 pages, latex, no figure

Superalgebras, constraints and partition functions

We consider Borcherds superalgebras obtained from semisimple finite-dimensional Lie algebras by adding an odd null root to the simple roots. The additional Serre relations can be expressed in a covariant way. The spectrum of generators at positive levels are associated to partition functions for a certain set of constrained bosonic variables, the constraints on which are complementary to the Serre relations in the symmetric product. We give some examples, focusing on superalgebras related to pure spinors, exceptional geometry and tensor hierarchies, of how construction of the content of the algebra at arbitrary levels is simplified.Comment: 27 pages. v2: Explanations and references added. Published versio

Quantization of Higher Spin Superfields in the anti-de Sitter Superspace

We describe a Lagrangian quantization of the free massless gauge superfield theories of higher superspins both in the anti-de Sitter and flat global superspaces.Comment: 9 pages, LaTe