Making use of a modified version, due to McCord, of the Dold-Thom construction of ordinary homology, we give a simple topological definition of a transfer for ramified covering maps in homology with arbitrary coefficients. The transfer is induced by a suitable map between topological groups. We also define a new cohomology transfer which is dual to the homology transfer. This duality allows us ...

We study isomorphism classes of symplectic dual pairs P ← S → P , where P is an integrable Poisson manifold, S is symplectic, and the two maps are complete, surjective Poisson submersions with connected and simply-connected fibres. For fixed P , these Morita self-equivalences of P form a group Pic(P ) under a natural “tensor product” operation. Variants of this construction are also studied, fo...

Portfolio analysis of the publication profile of a unit of interest, ranging from individuals, organizations, to a scientific field or interdisciplinary programs, aims to inform analysts and decision makers about the position of the unit, where it has been, and where it may go in a complex adaptive environment. A portfolio analysis may aim to identify the gap between the current position of an ...

The problem is to determine the homography H up to similarity which maps a point or line from a plane in the world to the image plane x́ = Hx. This is to be done using two different methods. For the first method, the projective error is first removed followed by the affine error using the provided coordinates of a rectangle and an additional orthogonal line pair. For the second method, five orth...

Combinatorially regular polyhedra are polyhedral realizations (embeddings) in Euclidean 3-space E of regular maps on (orientable) closed compact surfaces. They are close analogues of the Platonic solids. A surface of genus g > 2 admits only finitely many regular maps, and generally only a small number of them can be realized as polyhedra with convex faces. When the genus g is small, meaning tha...

In any concrete category C the natural problem of whether epimorphisms are surjective maps arise, as well as the dual problem of whether the monomorphisms are injective maps. This type of problems have already been studied before in several well known categories: for example in [6] it is shown that the property of epimorphisms of being surjective holds in the categories of von Neumann algebras,...

The Kneser-Hecke-operator is a linear operator defined on the complex vector space spanned by the equivalence classes of a family of self-dual codes of fixed length. It maps a linear self-dual code C over a finite field to the formal sum of the equivalence classes of those self-dual codes that intersect C in a codimension 1 subspace. The eigenspaces of this self-adjoint linear operator may be d...

The Cappell-Shaneson decomposition theorem for self-dual sheaves asserts that on a space with only even-codimensional strata any selfdual sheaf is cobordant to an orthogonal sum of twisted intersection chain sheaves associated to the various strata. In sharp contrast to this result, we prove that on a space with only odd-codimensional strata (not necessarily Witt), any self-dual sheaf is cobord...

Let r; n be xed natural numbers. We prove that for n-manifolds the set of all linear natural operators T ! T T (r) is a nitely dimensional vector space over R. We construct explicitly the bases of the vector spaces. As a corollary we nd all linear natural operators T ! T r. All manifolds and maps are assumed to be innnitely diierentiable. 0. Let r; n be xed natural numbers. Given a manifold M w...

We expose a new procedure of quantization of fields, based on the Geometric Langlands Correspondence. Starting from fields in the target space, we first reduce them to the case of fields on one-complex-variable target space, at the same time increasing the possible symmetry group G. Use the sigma model and momentum maps, we reduce the problem to a problem of quantization of trivial vector bundl...