Let $Φ\colon \sbat \times M \to M$ be a smooth action of the unit circle $ \sbat$ on a manifold . In this work, we compute the minimal model of in terms of the orbit space and the fixed point set , as a dg-module over the Sullivan's minimal model of .
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6 results for “DG-modules”
This thesis generalizes structures on -manifolds and Lie -algebroids.
problem Representation theory and linear structures of -manifolds and Lie -algebroids.
method Introduces differential graded modules and representations up to homotopy, defines Weil algebra, and studies VB-Lie -algebroids.
result Establishes an equivalence between VB-Lie -algebroids and -term representations up to homotopy of Lie -algebroids.
Develops Morse homology with DG coefficients for manifolds and spaces.
problem Homology with DG coefficients for manifolds and spaces.
method Derived local systems, DG modules, twisting cocycles, Morse trajectories.
result Isomorphic to DG Tor and Ext functors, recovers homology of total space of fibrations.
We define four versions of equivariant instanton Floer homology ( and ) for a class of 3-manifolds and -bundles over them including all rational homology spheres. These versions are analogous to the four flavors of monopole and Heegaard Floer homology theories. This construction…
This paper studies Hopf algebras from dg manifolds.
problem Understanding Hopf algebras from the perspective of dg manifolds.
method Analyzes the universal enveloping algebra of Lie algebra objects in homotopy categories of dg modules.
result The universal enveloping algebra of the Lie algebra object is a Hopf algebra.
Study spherical twists on K3 surfaces, compute their centers.
problem Understanding autoequivalence groups of K3 surfaces.
method Introduced spherical twists, studied their intersection numbers, and classified subgroups.
result Computed the center of autoequivalence groups of K3 surfaces.