41 citations · 300 across the 34 of their papers we have counts for
27 papers · 1 filter
Infinite homotopy stable class for 4-manifolds with boundary
Anthony Conway, Diarmuid Crowley, Mark Powell
We show that for every odd prime , there exists an infinite family of topological 4-manifolds that are all stably homeomorphic to one another, all the m…
Turning vector bundles
Diarmuid Crowley, Csaba Nagy, Blake Sims +1
We define a turning of a rank- vector bundle to be a homotopy of bundle automorphisms from , the identity of , to , minus the…
Simply-connected manifolds with large homotopy stable classes
Anthony Conway, Diarmuid Crowley, Mark Powell +1
For every and we construct pairwise homotopically inequivalent simply-connected, closed -dimensional manifolds, all of which are stably diffeomorphic…
Stably diffeomorphic manifolds and the realisation of modified surgery obstructions
Anthony Conway, Diarmuid Crowley, Mark Powell +1
For every we construct infinitely many -dimensional manifolds that are all stably diffeomorphic but pairwise not homotopy equivalent. Each of these manifolds has hyp…
Contact open books with flexible pages
Jonathan Bowden, Diarmuid Crowley
We give an elementary topological obstruction for a manifold of dimension to admit a contact open book with flexible Weinstein pages and : if t…
The derivative map for diffeomorphism of disks: An example
Diarmuid Crowley, Thomas Schick, Wolfgang Steimle
We prove that the derivative map , defined by taking the derivative of a diffeomorphism, can induce a nontrivial map on homotopy g…
The smooth classification of 4-dimensional complete intersections
Diarmuid Crowley, Csaba Nagy
We prove the "Sullivan Conjecture" on the classification of 4-dimensional complete intersections up to diffeomorphism. Here an -dimensional complete intersection is a smooth com…
Connected sum decompositions of high-dimensional manifolds
Imre Bokor, Diarmuid Crowley, Stefan Friedl +4
The classical Kneser-Milnor theorem says that every closed oriented connected 3-dimensional manifold admits a unique connected sum decomposition into manifolds that cannot be decom…
On the cardinality of the manifold set
Diarmuid Crowley, Tibor Macko
We study the cardinality of the set of manifolds homotopy equivalent to a given manifold M and compare it to the cardinality of the structure set of M.
Harmonic spinors and metrics of positive curvature via the Gromoll filtration and Toda brackets
Diarmuid Crowley, Thomas Schick, Wolfgang Steimle
We construct non-trivial elements of order 2 in the homotopy groups , for * congruent 1 or 2 modulo 8, which are detected by the "assembling homomorp…
Embeddings of non-simply-connected 4-manifolds in 7-space. I. Classification modulo knots
D. Crowley, A. Skopenkov
We work in the smooth category. Let be a closed connected orientable 4-manifold with torsion free , where . Our main result is a complete readily calculable…
An analytic invariant of G_2 manifolds
Diarmuid Crowley, Sebastian Goette, Johannes Nordström
We prove that the moduli space of holonomy G_2-metrics on a closed 7-manifold is in general disconnected by presenting a number of explicit examples. We detect different connected…
The topology of Stein fillable manifolds in high dimensions II
Jonathan Bowden, Diarmuid Crowley, András I. Stipsicz +1
We continue our study of contact structures on manifolds of dimension at least five using complex surgery theory. We show that in each dimension 2q+1 > 3 there are 'maximal' almost…
The classification of 2-connected 7-manifolds
Diarmuid Crowley, Johannes Nordström
We present a classification theorem for closed smooth spin 2-connected 7-manifolds M. This builds on the almost-smooth classification from the first author's thesis. The main addit…
The topology of Stein fillable manifolds in high dimensions I
Jonathan Bowden, Diarmuid Crowley, András I. Stipsicz
We give a bordism-theoretic characterisation of those closed almost contact (2q+1)-manifolds (with q > 2) which admit a Stein fillable contact structure. Our method is to apply Eli…
Finite group actions on Kervaire manifolds
Diarmuid Crowley, Ian Hambleton
The (4k+2)-dimensional Kervaire manifold is a closed, piecewise linear (PL) manifold with Kervaire invariant 1 and the same homology as the product of two (2k+1)-dimensional sphere…
New invariants of G_2-structures
Diarmuid Crowley, Johannes Nordström
We define a Z/48-valued homotopy invariant nu of a G_2-structure on the tangent bundle of a closed 7-manifold in terms of the signature and Euler characteristic of a coboundary wit…
The Gromoll filtration, KO-characteristic classes and metrics of positive scalar curvature
Diarmuid Crowley, Thomas Schick
Let X be a closed m-dimensional spin manifold which admits a metric of positive scalar curvature and let Pos(X) be the space of all such metrics. For any g in Pos(X), Hitchin used…
Functorial semi-norms on singular homology and (in)flexible manifolds
Diarmuid Crowley, Clara Loeh
A functorial semi-norm on singular homology is a collection of semi-norms on the singular homology groups of spaces such that continuous maps between spaces induce norm-decreasing…
Kreck-Stolz invariants for quaternionic line bundles
Diarmuid Crowley, Sebastian Goette
We generalise the Kreck-Stolz invariants s_2 and s_3 by defining a new invariant, the t-invariant, for quaternionic line bundles E over closed spin-manifolds M of dimension 4k-1 wi…
The additivity of the -invariant and periodicity in topological surgery
Diarmuid Crowley, Tibor Macko
For a closed topological manifold M with dim (M) >= 5 the topological structure set S(M) admits an abelian group structure which may be identified with the algebraic structure grou…
On the mapping class groups of $#_r(S^p \times S^p)$ for
Diarmuid Crowley
For M_r = #_r(S^p \times S^p), p=3, 7, we calculate the group of isotopy classes of orientation preserving diffeomorphisms of modulo isotopy classes with representatives whic…
The smooth structure set of
Diarmuid Crowley
We calculate the smooth structure set of , , for and . As a consequence we show that in general cannot admit a grou…
Stably diffeomorphic manifolds and l_{2q+1}(Z[π])
Diarmuid Crowley, Jörg Sixt
The monoids l_{2q+1}(Z[π]) detect s-cobordisms amongst certain bordisms between stably diffeomorphic 2q-dimensional manifolds and generalise the Wall simple surgery obstruction gro…