We give an upper bound for the rank r of homogeneous (even) Clifford structures on compact manifolds of non-vanishing Euler characteristic. More precisely, we show that if r = 2a · b with b odd, then r ≤ 9 for a = 0, r ≤ 10 for a = 1, r ≤ 12 for a = 2 and r ≤ 16 for a ≥ 3. Moreover, we describe the four limiting cases and show that there is exactly one solution in each case. 2010 Mathematics Su...

Viro method plays an important role in the study of topology of real algebraic hypersurfaces. The T -primitive hypersurfaces we study here appear as the result of Viro’s combinatorial patchworking when one starts with a primitive triangulation. We show that the Euler characteristic of the real part of such a hypersurface of even dimension is equal to the signature of its complex part. We use th...

We study those (2,m, n)-groups which are almost simple and for which the absolute value of the Euler characteristic is a product of two prime powers. All such groups which are not isomorphic to PSL2(q) or PGL2(q) are completely classified.

We identify a combinatorial quantity (the alternating sum of the h-vector) defined for any simple polytope as the signature of a toric variety. This quantity was introduced by R. Charney and M. Davis in their work, which in particular showed that its nonnegativity is closely related to a conjecture of H. Hopf on the Euler characteristic of a nonpositively curved manifold. We prove positive (or ...

The main question discussed in this paper is how well a finite metric space of size n can be embedded into a graph with certain topological restrictions. The existing constructions of graph spanners imply that any n-point metric space can be represented by a (weighted) graph with n vertices and n1+O(1/r) edges, with distances distorted by at most r . We show that this tradeoff between the numbe...

where for simplicity X+ denotes the suspension spectrum of the space obtained from X by adding a disjoint basepoint. One key property of τ(f) is the fact that the composite map f+ ·τ(f) : B+ −→ B+ induces a map on integral homology which is multiplication by the Euler characteristic χ(F ). The purpose of this paper is to construct something like the transfer τ(f) in many cases in which F is not...

Let Fg 1, g> 1, be the mapping class group consisting of all isotopy classes of base-point and orientation preserving homeomorphisms of a closed, oriented surface F of genus g. Let )~(~1) be its Euler characteristic in the sense of Wall, that is Z(F~I)= [Fgl: F] l z(E/F), where F is any torsion free subgroup of finite index in F~ 1 and E is a contractible space on which F acts freely and proper...

Let W be a crystallographic Weyl group, and let TW be the complex toric variety attached to the fan of cones corresponding to the reflecting hyperplanes of W , and its weight lattice. The real locus TW (R) is a smooth, connected, compact manifold with a W -action. We give a formula for the Euler characteristic of TW (R) as a generalised character of W . In type An−1 for n odd, one obtains a gen...

The Calderon problem for two-dimensional manifolds by the BC-method (a corrected version) As was shown by M.Lassas and G.Uhlmann (2001), the smooth two-dimensional compact orientable Riemann manifold with the boundary is uniquely determined by its Dirichlet-to-Neumann map up to conformal equivalence. We give a new proof of this fact based on relations between the Calderon problem and Function A...

We consider closed topological 4-manifolds M with universal cover S × S and Euler characteristic χ(M) = 1. All such manifolds with π = π1(M) ∼= Z/4 are homotopy equivalent. In this case, we show that there are four homeomorphism types, and propose a candidate for a smooth example which is not homeomorphic to the geometric quotient. If π ∼= Z/2×Z/2, we show that there are three homotopy types (a...