The equivalence of -groupoids and cubical -complexes
The Equivariant Bundle Subtraction Theorem and its applications
In the theory of transformation groups, it is important to know what kind of isotropy subgroups of G do occur at points of the space upon which the given group G acts. In this article, for a finite group G, we prove the Equivariant Bundle Subtraction Theorem (Theorem 2.2) which allows us to construct smooth G-manifolds with prescribed isotropy subgroups around the G-fixed point sets. In Theorem 0.1, we restate Oliver's result about manifolds M and G-vector bundles over M that occur, respectively,...
The equivariant Dehn's lemma and loop theorem.
The equivariant topological s-cobordism theorem.
The Equivariant Triangulation Theorem for Actions of Compact Lie Groups.
The eta Invariant and ...O of Lens Spaces.
The Euler characteristic and signature for open manifolds
The Euler Characteristic is the Unique Locally Determined Numerical Homotopy Invariant of Finite Complexes.
The Euler characteristic of a category.
The Euler characteristic of algebraic complete intersections.
The Euler class and periodicity of group cohomology.
The Euler-Poincaré-Hopf theorem for flat connections in some transitive Lie algebroids
This paper is a continuation of [19], [21], [22]. We study flat connections with isolated singularities in some transitive Lie algebroids for which either or or are isotropy Lie algebras. Under the assumption that the dimension of the isotropy Lie algebra is equal to , where is the dimension of the base manifold, we assign to any such isolated singularity a real number called an index. For -Lie algebroids, this index cannot be an integer. We prove the index theorem (the Euler-Poincaré-Hopf...
The existence of algebraic surfaces with preassigned Chern numbers.
The existence of critical values in an abstract perturbation problem.
The existence of maps of nonzero degree between aspherical 3-manifolds.
The existence of negatively Ricci curved metrics on three manifolds.
The existence of polar non-degenerate functions on a topological manifold
The extended complexity of three-manifolds.
The extension of Johnson's homomorphism form the Torelli group to the mapping class group.
The Finiteness Obstructions for Nilpotent Spaces lie in D (...).