Effective actions are derived for (2,0) and (2,1) superstrings by studying the corresponding sigma-models. The geometry is a generalisation of Kahler geometry involving torsion and the field equations imply that the curvature with torsion is self-dual in four dimensions, or has SU(n, m) holonomy in other dimensions. The Yang-Mills fields are self-dual in four dimensions and satisfy a form of th...

Motivated by conventional gauge theories, we consider a theory of gravity in which the Einstein–Hilbert action is replaced by a term that is quadratic in the Riemann tensor. We focus on cosmological solutions to the field equations in flat, open and closed universes. The gravitational action is scale invariant, so the only matter source considered is radiation. The theory can also accommodate i...

This paper gives a short summary of the central role played by Ed Brown’s “twisted cochains” in higher Franz-Reidemeister (FR) torsion and higher analytic torsion. Briefly, any fiber bundle gives a twisted cochain which is unique up to fiberwise homotopy equivalence. However, when they are based, the difference between two of them is a higher algebraic K-theory class measured by higher FR torsi...

We compute the moduli metrics of worldvolume 0-brane solitons of D-branes and the worldvolume self-dual string solitons of the M-5-brane and examine their geometry. We find that the moduli spaces of 0-brane solitons of D-4-branes and D-8-branes are hyper-Kähler manifolds with torsion and octonionic Kähler manifolds with torsion, respectively. The moduli space of the self-dual string soliton of ...

We obtain a general lower bound for the number of fixed points of a circle action on a compact almost complex manifold M of dimension 2n with nonempty fixed point set, provided the Chern number c1cn−1[M ] vanishes. The proof combines techniques originating in equivariant K-theory with celebrated number theory results on polygonal numbers, introduced by Pierre de Fermat. This lower bound confirm...

This paper gives a short summary of the central role played by Ed Brown’s “twisting cochains” in higher FranzReidemeister (FR) torsion and higher analytic torsion. Briefly, any fiber bundle gives a twisting cochain which is unique up to fiberwise homotopy equivalence. However, when they are based, the difference between two of them is a higher algebraic K-theory class measured by higher FR tors...

The gluing equations of a cusped hyperbolic 3-manifold M are a system of polynomial equations in the shapes of an ideal triangulation T of M that describe the complete hyperbolic structure of M and its deformations. Given a Neumann-Zagier datum (comprising the shapes together with the gluing equations in a particular canonical form) we define a formal power series with coefficients in the invar...

Abstract Let G be a compact connected Lie group, and let $\operatorname {Hom}({\mathbb {Z}}^m,G)$ the space of pairwise commuting m -tuples in . We study problem which primes $p \operatorname {Z}}^m,G)_1$ , component containing element $(1,\ldots ,1)$ has p -torsion homology. will prove that for $m\ge 2$ homology if only divides order Weyl group $G=SU(n)$ some exceptional groups. also compute t...

In the early seventies D. Ray and I. Singer [17] introduced the notion of zeta-regularized determinants. They used it to define the analytic version of Reidemeister torsion as an alternating product of determinants. One way to understand analytic torsion is to consider it as a ”multiplicative index” of an elliptic complex. By the L2-index theorem of M. Atiyah [1] this analogy suggests that one ...