Drawing on the classification of symplectic manifolds with cosiotropic principal orbits by Duistermaat and Pelayo, in this note we exhibit families of compact symplectic manifolds, such that (i) no two manifolds in a family are homotopically equivalent, (ii) each manifold in each family possesses Hamiltonian, and non-Hamiltonian, toric symmetries, (iii) each manifold has odd first Betti number ...

Using Kadeishvili’s [11] formulas with appropriate signs, we show that the classical cobar construction from coalgebras to algebras Ω : CoAlg → Alg can be enhanced to a functor from Hopf algebras to E2 algebras (for a certain choice of E2 operad) Ω : HopfAlg → E2Alg, which, unlike its classical counterpart, is not strictly adjoint, but homotopically equivalent to the left adjoint of the enhance...

We prove the existence of at least cl(M) periodic orbits for certain time dependant Hamiltonian systems on the cotangent bundle of an arbitrary compact manifold M . These Hamiltonians are not necessarily convex but they satisfy a certain boundary condition given by a Riemannian metric on M . We discretize the variational problem by decomposing the time 1 map into a product of “symplectic twist ...

Even when the fundamental group is intractable (i.e. not "good") many interesting 4-dimensional surgery problems have topological solutions. We unify and extend the known examples and show how they compare to the (presumed) counterexamples by reference to Dwyer's filtration on second homology. The development brings together many basic results on the nilpotent theory o f links. As a special cas...

It is argued that the gauge anomalies are only the artefacts of quantum field theory when certain subtleties are not taken into account. With the Berry's phase needed to satisfy certain boundary conditions of the generating path integral, the gauge anomalies associated with homotopically nontrivial gauge transformations are shown explicitly to be eliminated, without any extra quantum fields int...

Let G be a homotopically trivial and effective compact Lie group action on a compact manifold N of nonpositive curvature. Under certain assumptions on N we prove that if G has dimension equal to rank of Center π1(N), then G must be connected. Furthermore, if on N there exists a point having negative definite Ricci tensor, then we show that G is the trivial group.

We call a Gromov-Hausdorff limit of complete Riemannian manifolds with a lower bound of Ricci curvature a Ricci limit space. In this paper, we prove that any Ricci limit space has integral Hausdorff dimension provided that its Hausdorff dimension is not greater than two. We also classify one-dimensional Ricci limit spaces.

Let (Ω, d) be a metric space where Ω is a set with positive and finite Hausdorff outer measure in its Hausdorff dimension and let B be a partition of Ω. The coherent upper conditional prevision defined as the Choquet integral with respect to its associated Hausdorff outer measure is proven to satisfy the disintegration property and the conglomerative principle on every partition.

In this paper, two cardinal inequalities for functionally Hausdorff spaces are established. A bound on the cardinality of the τθ-closed hull of a subset of a functionally Hausdorff space is given. Moreover, the following theorem is proved: ifX is a functionally Hausdorff space, then |X| ≤ 2χ(X)wcd(X).

A flow of an open manifold is very complicated even if its orbit space is Hausdorff. In this paper, we define the strongly Hausdorff flows and consider their dynamical properties in terms of the orbit spaces. By making use of this characterization, we finally classify all the strongly Hausdorff C1-flows.