Related papers: Groups with torsion, bordism and rho-invariants

Let M be a complete n-dimensional Riemannian spin manifold, partitioned by q two-sided hypersurfaces which have a compact transverse intersection N and which in addition satisfy a certain coarse transversality condition. Let E be a…

A new local, covariant and nilpotent symmetry is shown to exist for the interacting BRST invariant U(1) gauge theory in two dimensions of space-time. Under this new symmetry, it is the gauge-fixing term that remains invariant and the…

Assume that the compact Riemannian spin manifold $(M^n,g)$ admits a $G$-structure with characteristic connection $\nabla$ and parallel characteristic torsion ($\nabla T=0$), and consider the Dirac operator $D^{1/3}$ corresponding to the…

We show that an enlargeable Riemannian metric on a (possibly nonspin) manifold cannot have uniformly positive scalar curvature. This extends a well-known result of Gromov and Lawson to the nonspin setting. We also prove that every…

Let $(N, J)$ be a simply connected $2n$-dimensional nilpotent Lie group endowed with an invariant complex structure. We define a left invariant Riemannian metric on $N$ compatible with $J$ to be minimal, if it minimizes the norm of the…

We consider a 4-dimensional Riemannian manifold M endowed with a right skew-circulant tensor structure S, which is an isometry with respect to the metric g and the fourth power of S is minus identity. We determine a class of manifolds (M,…

We introduce and study a notion of invariant intrinsic torsion geometry which appears, for instance, in connection with the Bryant-Salamon metric on the spinor bundle over S^3. This space is foliated by six-dimensional hypersurfaces, each…

Let $S$ be a compact, connected, oriented surface, possibly with boundary, of negative Euler characteristic. In this article we extend Lindenstrauss-Mirzakhani's and Hamenst\"adt's classification of locally finite mapping class group…

We study local structure of the moduli space of compact Einstein metrics with respect to the boundary conformal metric and mean curvature. In dimension three, we confirm M. Anderson's conjecture in a strong sense, showing that the map from…

We study de Rham cohomology for various differential calculi on finite groups G up to order 8. These include the permutation group S_3, the dihedral group D_4 and the quaternion group Q. Poincare' duality holds in every case, and under some…

We prove a gluing formula for the analytic torsion on non-compact (i.e. singular) riemannian manifolds. Let M= U\cup M_1, where M_1 is a compact manifold with boundary and U represents a model of the singularity. For general elliptic…

In this paper we prove that the compact Lie group $G_2$ admits a left-invariant Einstein metric that is not geodesic orbit. In order to prove the required assertion, we develop some special tools for geodesic orbit Riemannian manifolds. It…

We find a unique torsion free Riemannian spin connection for the natural Killing metric on the quantum group $C_q[SL_2]$, using a recent frame bundle formulation. We find that its covariant Ricci curvature is essentially proportional to the…

Using standard results from higher (secondary) index theory, we prove that the positive scalar curvature bordism groups of a cartesian product GxZ are infinite in dimension 4n if n>0 G a group with non-trivial torsion. We construct…

Given a metric measure space $(X,d,\mathfrak{m})$ that satisfies the Riemannian Curvature Dimension condition, $RCD^*(K,N),$ and a compact subgroup of isometries $G \leq Iso(X)$ we prove that there exists a $G-$invariant measure,…

The spinor representation of the Lorentz group does not accept simple generalization with the group GL(4,R) of general linear coordinate transformations. The Dirac equation may be written for an arbitrary choice of a coordinate system and a…

Let $M$ be an oriented closed 4-manifold and $\cL$ be a $spin^c$ structure on $M$. In this paper we prove that under a suitable condition the Seiberg-Witten moduli space has a canonical spin structure and its spin bordism class is an…

In this note we complete a study of globally homogeneous Riemannian quotients $\Gamma\backslash (M,ds^2)$ in positive curvature. Specifically, $M$ is a homogeneous space $G/H$ that admits a $G$-invariant Riemannian metric of strictly…

For a closed topological manifold M with dim (M) >= 5 the topological structure set S(M) admits an abelian group structure which may be identified with the algebraic structure group of M as defined by Ranicki. If dim (M) = 2d-1, M is…

We prove that if an orientable 3-manifold $M$ admits a complete Riemannian metric whose scalar curvature is positive and has at most $C$-quadratic decay at infinity for some $C > \frac{2}{3}$, then it decomposes as a (possibly infinite)…