Chain homotopy pullbacks and pushouts
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.
Si fa vedere che alcune classi di Chern di fibrati vettoriali complessi possono essere costruite non solo partendo da connessioni ma, sotto certe condizioni, anche da connessioni lineari singolari. Nel caso particolare del fibrato tangente possono essere costruite anche a partire da metriche singolari. Viene fatto uso in modo essenziale della -coomologia di de Rham (introdotta da Cheeger e Teleman).