Let M be a compact connected Fujiki manifold, G semisimple affine algebraic group over C with one simple factor and P fixed proper parabolic subgroup of G. For holomorphic principal G–bundle EG M, let EP the P–bundle EG⟶EG/P given by quotient map. We prove that following three statements are equivalent: (1) ad(EG) is numerically flat, (2) line bundle ⋀topad(EP)⁎ nef, (3) for every reduced irred...

We find the conditions under which a Riemannian manifold equipped with a closed threeform and a vector field define an on–shell N = (2, 2) supersymmetric gauged sigma model. The conditions are that the manifold admits a twisted generalized Kähler structure, that the vector field preserves this structure, and that a so–called generalized moment map exists for it. By a theorem in generalized comp...

Let T{t) be a Co-semigroup of linear operators on a Banach space X, and let X® , resp. X® , denote the closed subspaces of X" consisting of all functionals x* such that the map t •-» T*{t)x* is strongly continuous for t > 0, resp. t > 0. Theorem. Every nonzero orbit of the quotient semigroup on X*/X® is nonseparably valued. In particular, orbits in X*/X® are either zero for t > 0 or nonseparabl...

We have seen that the proof of existence of inverses for elements of Ext(X) can be based on a lifting theorem for (completely) positive maps of C(X) into a quotient C∗-algebra of the form E/K, where E ⊆ B(H) is a C∗-algebra containing the compact operators K. That argument works equally well for arbitrary C∗-algebras in place of C(X) whenever a completely positive lifting exists. Thus we are le...

Let Knots be the abelian monoid of isotopy classes of knots S ⊂ S under connected sum, and let C be the topological knot concordance group of knots modulo slice knots. Cochran-OrrTeichner [COT03] defined a filtration of C: C ⊃ F(0) ⊃ F(0.5) ⊃ F(1) ⊃ F(1.5) ⊃ F(2) ⊃ . . . The quotient C/F(0.5) is isomorphic to Levine’s algebraic concordance group AC1 [Lev69]; F(0.5) is the algebraically slice kn...

In this paper we introduce techniques from complex harmonic analysis to prove a weaker version of the Geometric Arveson-Douglas Conjecture on the Bergman space for a complex analytic subset that is smooth on the boundary of the unit ball and intersects transversally with it. In fact, we prove that the projection operator onto the corresponding quotient module is in the Toeplitz algebra T (L∞), ...

In this paper, all the monoids considered are commutative. If S is a monoid generated by {m1, . . . ,mn}, then S is isomorphic to a quotient monoid of N by the kernel congruence σ of the map φ : N → S, φ(k1, . . . , kn) = ∑n i=1 kimi. Under this setting, a finite presentation for S is a finite subset ρ of Nn×Nn such that the congruence generated by ρ is equal to σ. Rédei proves in [5] that ever...

The only proof of this I know is kind of fiddly and not enlightening. But the point is that in most categories that appear ‘in nature,’ regular, strong, and extremal epics are about the same, and all are the correct notion of quotient, while ordinary epimorphisms may not be. For example, N→ Q is epic in Rings, but not extremal epic. In Top the epics are the surjective maps, while the regular = ...

It is an open problem whether an infinite-dimensional amenable Banach algebra exists whose underlying Banach space is reflexive. We give sufficient conditions for a reflexive, amenable Banach algebra to be finite-dimensional (and thus a finite direct sum of full matrix algebras). If A is a reflexive, amenable Banach algebra such that for each maximal left ideal L of A (i) the quotient A/L has t...