Realizing modules over the homology of a DGA

Let A be a DGA over a field and X a module over H_*(A). Fix an $A_\infty$-structure on H_*(A) making it quasi-isomorphic to A. We construct an equivalence of categories between A_{n+1}-module structures on X and length n Postnikov systems in the derived category of A-modules based on the bar resolution of X. This implies that quasi-isomorphism classes of A_n-structures on X are in bijective correspondence with weak equivalence classes of rigidifications of the first n terms of the bar resolution of X to a complex of A-modules. The above equivalences of categories are compatible for different values of n. This implies that two obstruction theories for realizing X as the homology of an A-module coincide.Comment: 24 page

On quaternionic line bundles

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1999.Includes bibliographical references (p. 35).by Gustavo Granja.Ph.D

Self maps of quaternionic projective spaces

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1997.Includes bibliographical references (leaves 22-23).by Gustavo Granja.M.S

Givental's non-linear Maslov index on lens spaces

Givental's non-linear Maslov index, constructed in 1990, is a quasimorphism on the universal cover of the identity component of the contactomorphism group of real projective space. This invariant was used by several authors to prove contact rigidity phenomena such as orderability, unboundedness of the discriminant and oscillation metrics, and a contact geometric version of the Arnold conjecture. In this article we give an analogue for lens spaces of Givental's construction and its applications.Comment: 44 pages; v3: minor changes; v2: besides minor changes, we corrected a mistake in Corollary 1.3(iv

Homotopy decomposition of a group of symplectomorphisms of S2×S2

AbstractWe continue the analysis started by Abreu, McDuff and Anjos of the topology of the group of symplectomorphisms of S2×S2 when the ratio of the area of the two spheres lies in the interval (1,2]. We express the group, up to homotopy, as the pushout (or amalgam) of certain of its compact Lie subgroups. We use this to compute the homotopy type of the classifying space of the group of symplectomorphisms and the corresponding ring of characteristic classes for symplectic fibrations