28 research outputs found
The Geography of Non-formal Manifolds
We show that there exist non-formal compact oriented manifolds of dimension
and with first Betti number if and only if and
, or and . Moreover, we present explicit
examples for each one of these cases.Comment: 8 pages, one reference update
(Contravariant) Koszul duality for DG algebras
A DG algebras over a field with connected and
has a unique up to isomorphism DG module with . It is proved
that if is degreewise finite, then RHom_A(?,K): D^{df}_{+}(A)^{op}
\equiv D_{df}^{+}}(RHom_A(K,K)) is an exact equivalence of derived categories
of DG modules with degreewise finite-dimensional homology. It induces an
equivalences of and the category of perfect DG
-modules, and vice-versa. Corresponding statements are proved also
when is simply connected and .Comment: 33 page
Massey products in symplectic manifolds
The paper is devoted to study of Massey products in symplectic manifolds.
Theory of generalized and classical Massey products and a general construction
of symplectic manifolds with nontrivial Massey products of arbitrary large
order are exposed. The construction uses the symplectic blow-up and is based on
the author results, which describe conditions under which the blow-up of a
symplectic manifold X along its submanifold Y inherits nontrivial Massey
products from X ot Y. This gives a general construction of nonformal symplectic
manifolds.Comment: LaTeX, 48 pages, 2 figure
The Dold-Kan Correspondence and Coalgebra Structures
By using the Dold-Kan correspondence we construct a Quillen adjunction
between the model categories of non-cocommutative coassociative simplicial and
differential graded coalgebras over a field. We restrict to categories of
connected coalgebras and prove a Quillen equivalence between them.Comment: 24 pages. Accepted by the Journal of Homotopy and Related Structures.
Online 28 November 201
Assembly maps with coefficients in topological algebras and the integral K-theoretic Novikov conjecture
We prove that any countable discrete and torsion free subgroup of a general
linear group over an arbitrary field or a similar subgroup of an almost
connected Lie group satisfies the integral algebraic K-theoretic (split)
Novikov conjecture over \cpt and \S, where \cpt denotes the C^*-algebra of
compact operators and \S denotes the algebra of Schatten class operators. We
introduce assembly maps with finite coefficients and under an additional
hypothesis, we prove that such a group also satisfies the algebraic K-theoretic
Novikov conjecture over \bar{\mathbb{Q}} and \mathbb{C} with finite
coefficients. For all torsion free Gromov hyperbolic groups G, we demonstrate
that the canonical algebra homomorphism \cpt[G]\map C^*_r(G)\hat{\otimes}\cpt
induces an isomorphism between their algebraic K-theory groups.Comment: v2 Exposition improved; one lemma and grant acknowledgement added; v3
some terminology changed and details added, Theorems 4.5 and 4.7 in v3 need
an extra hypothesis; v4 abridged version accepted for publication in JHR
Functorial homotopy decompositions of looped co-H spaces
In recent work of the first and third authors, functorial coalgebra decompositions of tensor algebras were geometrically realized to give functorial homotopy decompositions of loop suspensions. Later work by all three authors generalized this to functorial decompositions of looped coassociative co-H spaces. In this paper we use different methods which allow for the coassociative hypothesis to be removed
Enterprise policymaking in the UK : prescribed approaches and day-to-day practice
This chapter looks at enterprise policymaking in the UK and the prescribed approaches and day-to-day practic