307 research outputs found
Changing the world one researcher at a time: a skills and engagement approach to library research support
The Research Skills Team in the Library at the University of Birmingham is a unique formation of librarians, a postgraduate skills officer and postgraduate teaching assistants.
The team’s clear focus is the researcher themselves, and their ‘lived experience’, from the moment of registration on a PhD course, through post-doctoral early career posts, to lecturer and professor level.
The team’s mission is to be a seamless interface to the research services offered by the library, to demystify the increasingly complex scholarly communication system, and to advocate for initiatives such as open research.
By taking a holistic approach to the researcher experience and orienting services accordingly, and by safeguarding staff time to finesse an ongoing suite of training opportunities, the library is demonstrating an ongoing commitment to facilitate high quality research
Some recent approaches in 4-dimensional surgery theory
It is well-known that an n-dimensional Poincar\'{e} complex , ,
has the homotopy type of a compact topological -manifold if the total
surgery obstruction vanishes. The present paper discusses recent
attempts to prove analogous result in dimension 4. We begin by reviewing the
necessary algebraic and controlled surgery theory. Next, we discuss the key
idea of Quinn's approach. Finally, we present some cases of special fundamental
groups, due to the authors and to Yamasaki
The Bryant-Ferry-Mio-Weinberger construction of generalized manifolds
Following Bryant, Ferry, Mio and Weinberger we construct generalized
manifolds as limits of controlled sequences p_i: X_i --> X_{i-1} : i = 1,2,...
of controlled Poincar\'e spaces. The basic ingredient is the
epsilon-delta-surgery sequence recently proved by Pedersen, Quinn and Ranicki.
Since one has to apply it not only in cases when the target is a manifold, but
a controlled Poincar\'e complex, we explain this issue very roughly.
Specifically, it is applied in the inductive step to construct the desired
controlled homotopy equivalence p_{i+1}: X_{i+1} --> X_i. Our main theorem
requires a sufficiently controlled Poincar\'e structure on X_i (over X_{i-1}).
Our construction shows that this can be achieved. In fact, the Poincar\'e
structure of X_i depends upon a homotopy equivalence used to glue two manifold
pieces together (the rest is surgery theory leaving unaltered the Poincar\'e
structure). It follows from the epsilon-delta-surgery sequence (more precisely
from the Wall realization part) that this homotopy equivalence is sufficiently
well controlled. In the final section we give additional explanation why the
limit space of the X_i's has no resolution.Comment: This is the version published by Geometry & Topology Monographs on 22
April 200
Applications of controlled surgery in dimension 4: Examples
The validity of Freedman's disk theorem is known to depend only on the
fundamental group. It was conjectured that it fails for nonabelian free
fundamental groups. If this were true then surgery theory would work in
dimension four. Recently, Krushkal and Lee proved a surprising result that
surgery theory works for a large special class of 4-manifolds with free
nonabelian fundamental groups. The goal of this paper is to show that this also
holds for other fundamental groups which are not known to be good, and that it
is best understood using controlled surgery theory of Pedersen--Quinn--Ranicki.
We consider some examples of 4-manifolds which have the fundamental group
either of a closed aspherical surface or of a 3-dimensional knot space. A more
general theorem is stated in the appendix
Controlled surgery and -homology
This paper presents an alternative approach to controlled surgery
obstructions. The obstruction for a degree one normal map with control map to complete controlled
surgery is an element , where are topological manifolds of dimension . Our proof uses
essentially the geometrically defined -spectrum as described by
Nicas (going back to Quinn) and some well known homotopy theory. We also
outline the construction of the algebraically defined obstruction, and we
explicitly describe the assembly map in terms of forms in the case . Finally, we
explicitly determine the canonical map
On minimal Poincar\'{e} -complexes
We consider two types of minimal Poincar\'e -complexes. One is defined
with respect to the degree -map order. This idea was already present in our
previous papers, and more systematically studied later by Hillman. The second
type of minimal Poincar\'e -complexes were introduced by Hambleton, Kreck
and Teichner. It is not based on an order relation. In the present paper we
study existence and uniqueness
s-Cobordism classification of -manifolds through the group of homotopy self-equivalences
The aim of this paper is to give an -cobordism classification of
topological -manifolds in terms of the standard invariants using the group
of homotopy self-equivalences. Hambleton and Kreck constructed a braid to study
the group of homotopy self-equivalences of -manifolds. Using this braid
together with the modified surgery theory of Kreck, we give an -cobordism
classification for certain -manifolds with fundamental group , such
that cd
Homotopy classification of -complexes relative an order relation
We define an order relation among oriented -complexes. We show that
with respect to this relation, two -complexes over the same complex are
homotopy equivalent if and only if there is an isometry between the second
homology groups. We also consider minimal objects of this relation.Comment: Monatsh. Math. (2015
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