Chain Complexes and Assembly.
Given a principal ideal domain of characteristic zero, containing 1/2, and a two-cone of appropriate connectedness and dimension, we present a sufficient algebraic condition, in terms of Adams-Hilton models, for the Hopf algebra to be isomorphic with the universal enveloping algebra of some -free graded Lie algebra; as usual, stands for free part, for homology, and for the Moore loop space functor.
In this work we compute the Chen–Ruan cohomology of the moduli spaces of smooth and stable -pointed curves of genus . In the first part of the paper we study and describe stack theoretically the twisted sectors of and . In the second part, we study the orbifold intersection theory of . We suggest a definition for an orbifold tautological ring in genus , which is a subring of both the Chen–Ruan cohomology and of the stringy Chow ring.
Let V be an orthogonal representation of a compact Lie group G and let S(V),D(V) be the unit sphere and disc of V, respectively. If F: V → ℝ is a G-invariant C¹-map then the G-equivariant gradient C⁰-map ∇F: V → V is said to be admissible provided that . We classify the homotopy classes of admissible G-equivariant gradient maps ∇F: (D(V),S(V)) → (V,V∖0).
The main result of the present paper is a classification theorem for finite-sheeted covering mappings over connected paracompact spaces. This theorem is a generalization of the classical classification theorem for covering mappings over a connected locally pathwise connected semi-locally 1-connected space in the finite-sheeted case. To achieve the result we use the classification theorem for overlay structures which was recently proved by S. Mardesic and V. Matijevic (Theorems 1 and 4 of [5]).