29 research outputs found
The Free Loop Space Homology of -connected -manifolds
Our goal in this paper is to compute the integral free loop space homology of
-connected -manifolds , . We do this when ,
or when and has trivial cup product squares, though
the techniques used here should extend to a much wider range of manifolds. We
also give partial information concerning the action of the Batalin-Vilkovisky
operator.Comment: JHR
Configuration Spaces and Polyhedral Products
This paper aims to find the most general combinatorial conditions under which
a moment-angle complex is a co--space, thus splitting unstably
in terms of its full subcomplexes. In this way we study to which extent the
conjecture holds that a moment-angle complex over a Golod simplicial complex is
a co--space. Our main tool is a certain generalisation of the theory of
labelled configuration spaces.Comment: Published in Advances in Mathematics, 201
The Loop Space Homotopy Type of Simply-connected Four-manifolds and their Generalizations
We determine loop space decompositions of simply-connected four-manifolds,
-connected -dimensional manifolds provided , and
connected sums of products of two spheres. These are obtained as special cases
of a more general loop space decomposition of certain torsion-free
-complexes with well-behaved skeleta and some Poincar\'{e} duality
features.Comment: Adv. Math., to be publishe
-Category of Moment-Angle Manifolds, Massey Products, and a Generalization of the Golod Property
We give various bounds for the Lusternik-Schnirelmann category of
moment-angle complexes and show how this relates to vanishing of Massey
products in . In particular, we
characterise the Lusternik-Schnirelmann category of moment-angle manifolds
over triangulated -spheres for , as well as
higher dimension spheres built up via connected sum, join, and vertex doubling
operations. This characterisation is given in terms of the combinatorics of
, the cup product length of , as well as a certain
generalisation of the Golod property. Some applications include information
about the category and vanishing of Massey products for moment-angle complexes
over fullerenes and -neighbourly complexes.Comment: New examples adde
Homotopy Decompositions of Looped Stiefel manifolds, and their Exponents
Let be an odd prime, and fix integers and such that . We give a -local homotopy decomposition for the loop space of
the complex Stiefel manifold . Similar decompositions are given for
the loop space of the real and symplectic Stiefel manifolds. As an application
of these decompositions, we compute upper bounds for the -exponent of
. Upper bounds for -exponents in the stable range and
are computed as well
LS-category of moment-angle manifolds, Massey products, and a generalisation of the Golod property
This paper is obtained as as synergy of homotopy theory, commutative algebra and combinatorics. We give various bounds for the Lusternik-Schnirelmann category of moment-angle complexes and show how this relates to vanishing of Massey products in Tor+R[v1,...,vn] (R [K], R) for the Stanley-Reisner ring R[K]. In particular, we characterise the Lusternik-Schnirelmann category of moment-angle manifolds ZK over triangulated d-spheres K for d ≤ 2, as well as higher dimension spheres built up via connected sum, join, and vertex doubling operations. This characterisation is given in terms of the combinatorics of K, the cup product length of H* (ZK), as well as a certain generalisation of the Golod property. As an application, we describe conditions for vanishing of Massey products in the case of fullerenes and k-neighbourly complexes