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6 results for “dg-modules”

Equivariant instanton homologymath.GT

New instanton homology theories for 3-manifolds and bundles.

problem Defining instanton homology for a class of 3-manifolds and bundles.

method Functorial construction for 4-manifold cobordisms, algebraic construction of homology theories for dg-modules.

result Isomorphic to Floer's instanton homology for admissible bundles, calculates

I^\infty

in all cases it is defined.

instanton homology 3-manifolds bundles functorial dg-modules

2019-07-01abs ↗pdf ↗

Minimal Models for Non-Free Circle Actionsmath.AT

Let $Φ\colon \sbat \times M \to M$ be a smooth action of the unit circle $ \sbat$ on a manifold $M$ . In this work, we compute the minimal model of $M$ in terms of the orbit space $B$ and the fixed point set $F\subset B$ , as a dg-module over the Sullivan's minimal model of $B$ .

2000-04-23abs ↗pdf ↗

\mathbb{Z}

-graded supergeometry: Differential graded modules, higher algebroid representations, and linear structuresmath.DG

This thesis generalizes structures on $\mathcal{Q}$ -manifolds and Lie $n$ -algebroids.

problem Representation theory and linear structures of

\mathcal{Q}

-manifolds and Lie

n

-algebroids.

method Introduces differential graded modules and representations up to homotopy, defines Weil algebra, and studies VB-Lie

n

-algebroids.

result Establishes an equivalence between VB-Lie

n

-algebroids and

(n+1)

-term representations up to homotopy of Lie

n

-algebroids.

$\mathcal{Q}$-manifolds Lie $n$-algebroids DG-modules representations up to homotopy Weil algebra

2021-06-28abs ↗pdf ↗

Morse homology with DG coefficientsmath.SG

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.

Morse homology derived local systems DG modules twisting cocycles Floer theory

2023-08-11abs ↗pdf ↗

Hopf algebras arising from dg manifoldsmath.DG

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.

dg manifolds Hopf algebras Lie algebroids homotopy categories universal enveloping algebra

2019-11-04abs ↗pdf ↗

Spherical twists, relations and the center of autoequivalence groups of K3 surfacesmath.AG

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.

K3 surfaces spherical twists autoequivalence groups derived categories intersection numbers

2022-10-01abs ↗pdf ↗