13 citations · 40 across the 11 of their papers we have counts for
20 papers
A ddc-type condition beyond the Kähler realm
Jonas Stelzig, Scott O. Wilson
This paper introduces a generalization of the ddc-condition for complex manifolds. Like the dd^c-condition, it admits a diverse collection of characterizations, and is hereditary u…
Hodge-de Rham numbers of almost complex 4-manifolds
Joana Cirici, Scott O. Wilson
We introduce and study Hodge-de Rham numbers for compact almost complex 4-manifolds, generalizing the Hodge numbers of a complex surface. The main properties of these numbers in th…
Almost complex manifolds with small Nijenhuis tensor
Luis Fernandez, Tobias Shin, Scott O. Wilson
We give several explicit examples of compact manifolds with a -parameter family of almost complex structures having arbitrarily small Nijenhuis tensor in the -norm. The …
Almost Hermitian Identities
Joana Cirici, Scott O. Wilson
We study the local commutation relation between the Lefschetz operator and the exterior differential on an almost complex manifold with a compatible metric. The identity that we ob…
Harmonic symmetries for Hermitian manifolds
Scott O. Wilson
Complex manifolds with compatible metric have a naturally defined subspace of harmonic differential forms that satisfy Serre, Hodge, and conjugation duality, as well as hard Lefsch…
Dolbeault cohomology for almost complex manifolds
Joana Cirici, Scott O. Wilson
This paper extends Dolbeault cohomology and its surrounding theory to arbitrary almost complex manifolds. We define a spectral sequence converging to ordinary cohomology, whose fir…
Topological and geometric aspects of almost Kähler manifolds via harmonic theory
Joana Cirici, Scott O. Wilson
The well-known Kähler identities naturally extend to the non-integrable setting. This paper deduces several geometric and topological consequences of these extended identities for…
Center of mass and Kähler structures
Scott O. Wilson, Mahmoud Zeinalian
There is a sequence of positive numbers , such that for any connected -dimensional Riemannian manifold , there are two mutually exclusive possibilities: There i…
Results Concerning Almost Complex Structures on the Six-Sphere
Scott O. Wilson
For the standard metric on the six-dimensional sphere, with Levi-Civita connection , we show there is no almost complex structure such that and $\nabla_{JX…
Differential K-theory as equivalence classes of maps to Grassmannians and unitary groups
Thomas Tradler, Scott O. Wilson, Mahmoud Zeinalian
We construct a model of differential K-theory, using the geometrically defined Chern forms, whose cocycles are certain equivalence classes of maps into the Grassmannians and unitar…
A loop group extension of the odd Chern character
Scott O. Wilson
We show that the universal odd Chern form, defined on the stable unitary group , extends to the loop group in a way that is closed with respect to an equivariant-type diffe…
Pseudodeterminants and perfect square spanning tree counts
Jeremy L. Martin, Molly Maxwell, Victor Reiner +1
The pseudodeterminant of a square matrix is the last nonzero coefficient in its characteristic polynomial; for a nonsingular matrix, this is just the determinant…
An Elementary Differential Extension of Odd K-theory
Thomas Tradler, Scott O. Wilson, Mahmoud Zeinalian
There is an equivalence relation on the set of smooth maps of a manifold into the stable unitary group, defined using a Chern-Simons type form, whose equivalence classes form an ab…
Loop Differential K-theory
Thomas Tradler, Scott O. Wilson, Mahmoud Zeinalian
In this paper we introduce an equivariant extension of the Chern-Simons form, associated to a path of connections on a bundle over a manifold M, to the free loop space LM, and show…
Homotopy DG algebras induce homotopy BV algebras
John Terilla, Thomas Tradler, Scott O. Wilson
Let TA denote the space underlying the tensor algebra of a vector space A. In this short note, we show that if A is a differential graded algebra, then TA is a differential Batalin…
Equivariant holonomy for bundles and abelian gerbes
Thomas Tradler, Scott O. Wilson, Mahmoud Zeinalian
This paper generalizes Bismut's equivariant Chern character to the setting of abelian gerbes. In particular, associated to an abelian gerbe with connection, an equivariantly closed…
Differential forms, fluids, and finite models
Scott O. Wilson
By rewriting the Navier-Stokes equation in terms of differential forms we give a formulation which is abstracted and reproduced in a finite dimensional setting. We give two example…
Free frobenius algebra on the differential forms of a manifold
Scott O. Wilson
We construct an action of a free resolution of the Frobenius properad on the differential forms of a closed oriented manifold. As a consequence, the forms of a manifold with values…
Geometric Structures on the Cochains of a Manifold
Scott O. Wilson
In this paper we develop several algebraic structures on the simplicial cochains of a triangulated manifold that are analogues of objects in differential geometry. We study a cocha…
Rectifying Partial Algebras Over Operads of Complexes
Scott O. Wilson
In this paper we prove that, in the category of chain complexes, partial algebras can be functorially replaced by quasi-isomorphic algebras. In particular, partial algebras contain…