The Geography of Non-formal Manifolds

We show that there exist non-formal compact oriented manifolds of dimension $n$ and with first Betti number $b_1=b\geq 0$ if and only if $n\geq 3$ and $b\geq 2$, or $n\geq (7-2b)$ and $0\leq b\leq 2$. 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 $A$ over a field $k$ with $H(A)$ connected and $H_{<0}(A)=0$ has a unique up to isomorphism DG module $K$ with $H(K)\cong k$. It is proved that if $H(A)$ 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 $D^{df}_{b}(A)^{op}$ and the category of perfect DG $RHom_A(K,K)$-modules, and vice-versa. Corresponding statements are proved also when $H(A)$ is simply connected and $H^{<0}(A)=0$.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