Poisson geometry of certain moduli spaces
Aspherical 2-Complexes and an Unsettled Problem of J. H. C. Whitehead.
Poisson geometry of flat connections for SU(2)-bundles on surfaces.
The singularities of Yang-Mills connections for bundles on a surface.
The singularities of Yang-Mills connections for bundles on a surface.
The Homotype Type of a Combinatorially Aspherical Presentation.
Poisson cohomology and quantization.
Crossed n-folds extensions of groups and cohomology.
The first k-invariant, Quillen's space BG+ and the construction of Kann and Thurston.
Group extensions, crossed pairs and an eight term exact sequence.
Differential Batalin-Vilkovisky algebras arising from twilled Lie-Rinehart algebras
Twilled L(ie-)R(inehart)-algebras generalize, in the Lie-Rinehart context, complex structures on smooth manifolds. An almost complex manifold determines an "almost twilled pre-LR algebra", which is a true twilled LR-algebra iff the almost complex structure is integrable. We characterize twilled LR structures in terms of certain associated differential (bi)graded Lie and G(erstenhaber)-algebras; in particular the G-algebra arising from an almost complex structure is a (strict) d(ifferential) G-algebra...
Poisson structures on certain moduli spaces for bundles on a surface
Let be a closed surface, a compact Lie group, with Lie algebra , and a principal -bundle. In earlier work we have shown that the moduli space of central Yang-Mills connections, with reference to appropriate additional data, is stratified by smooth symplectic manifolds and that the holonomy yields a homeomorphism from onto a certain representation space , in fact a diffeomorphism, with reference to suitable smooth structures and , where denotes the universal central extension of...
Lie-Rinehart algebras, Gerstenhaber algebras and Batalin-Vilkovisky algebras
For any Lie-Rinehart algebra , B(atalin)-V(ilkovisky) algebra structures on the exterior -algebra correspond bijectively to right -module structures on ; likewise, generators for the Gerstenhaber algebra correspond bijectively to right -connections on . When is projective as an -module, given a B-V algebra structure on , the homology of the B-V algebra coincides with the homology of with coefficients in with reference to the right -module structure determined by . When...
Singular Poisson-Kähler geometry of certain adjoint quotients
The Kähler quotient of a complex reductive Lie group relative to the conjugation action carries a complex algebraic stratified Kähler structure which reflects the geometry of the group. For the group SL(n,ℂ), we interpret the resulting singular Poisson-Kähler geometry of the quotient in terms of complex discriminant varieties and variants thereof.
Small models for chain algebras.
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