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"Rea, Simon"
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Homotopy types of$${{\\textrm{Spin}}}^{{\\textrm{c}}}(n)$$ -gauge groups over$$S^4
The gauge group of a principal G -bundle P over a space X is the group of G -equivariant homeomorphisms of P that cover the identity on X . We consider the gauge groups of bundles over$$S^4$$S 4 with$${{\\textrm{Spin}}}^{{\\textrm{c}}}(n)$$Spin c ( n ) , the complex spin group, as structure group and show how the study of their homotopy types reduces to that of$${{\\textrm{Spin}}}(n)$$Spin ( n ) -gauge groups over$$S^4$$S 4 . We then advance on what is known by providing a partial classification for$${{\\textrm{Spin}}}(7)$$Spin ( 7 ) - and$${{\\textrm{Spin}}}(8)$$Spin ( 8 ) -gauge groups over$$S^4$$S 4 .
Journal Article
Homotopy types of Spinc(n)-gauge groups over S4
The gauge group of a principal
G
-bundle
P
over a space
X
is the group of
G
-equivariant homeomorphisms of
P
that cover the identity on
X
. We consider the gauge groups of bundles over
S
4
with
Spin
c
(
n
)
, the complex spin group, as structure group and show how the study of their homotopy types reduces to that of
Spin
(
n
)
-gauge groups over
S
4
. We then advance on what is known by providing a partial classification for
Spin
(
7
)
- and
Spin
(
8
)
-gauge groups over
S
4
.
Journal Article
ISMAR: an airborne submillimetre radiometer
The International Submillimetre Airborne Radiometer (ISMAR) has been developed as an airborne demonstrator for the Ice Cloud Imager (ICI) that will be launched on board the next generation of European polar-orbiting weather satellites in the 2020s. It currently has 15 channels at frequencies between 118 and 664 GHz which are sensitive to scattering by cloud ice, and additional channels at 874 GHz are being developed. This paper presents an overview of ISMAR and describes the algorithms used for calibration. The main sources of bias in the measurements are evaluated, as well as the radiometric sensitivity in different measurement scenarios. It is shown that for downward views from high altitude, representative of a satellite viewing geometry, the bias in most channels is less than ±1 K and the NEΔT is less than 2 K, with many channels having an NEΔT less than 1 K. In-flight calibration accuracy is also evaluated by comparison of high-altitude zenith views with radiative-transfer simulations.
Journal Article
Homotopy types of gauge groups of PU(p)-bundles over spheres
We examine the relation between the gauge groups of
SU
(
n
)
- and
PU
(
n
)
-bundles over
S
2
i
, with
2
≤
i
≤
n
, particularly when
n
is a prime. As special cases, for
PU
(
5
)
-bundles over
S
4
, we show that there is a rational or
p
-local equivalence
G
2
,
k
≃
(
p
)
G
2
,
l
for any prime
p
if, and only if,
(
120
,
k
)
=
(
120
,
l
)
, while for
PU
(
3
)
-bundles over
S
6
there is an integral equivalence
G
3
,
k
≃
G
3
,
l
if, and only if,
(
120
,
k
)
=
(
120
,
l
)
.
Journal Article
Homotopy types of gauge groups of$$\\mathrm {PU}(p)$$ -bundles over spheres
We examine the relation between the gauge groups of$$\\mathrm {SU}(n)$$SU ( n ) - and$$\\mathrm {PU}(n)$$PU ( n ) -bundles over$$S^{2i}$$S 2 i , with$$2\\le i\\le n$$2 ≤ i ≤ n , particularly when n is a prime. As special cases, for$$\\mathrm {PU}(5)$$PU ( 5 ) -bundles over$$S^4$$S 4 , we show that there is a rational or p -local equivalence$$\\mathcal {G}_{2,k}\\simeq _{(p)}\\mathcal {G}_{2,l}$$G 2 , k ≃ ( p ) G 2 , l for any prime p if, and only if,$$(120,k)=(120,l)$$( 120 , k ) = ( 120 , l ) , while for$$\\mathrm {PU}(3)$$PU ( 3 ) -bundles over$$S^6$$S 6 there is an integral equivalence$$\\mathcal {G}_{3,k}\\simeq \\mathcal {G}_{3,l}$$G 3 , k ≃ G 3 , l if, and only if,$$(120,k)=(120,l)$$( 120 , k ) = ( 120 , l ) .
Journal Article
Homotopy Types of Gauge Groups of Principal Bundles with Certain Non-Simply Connected Structure Groups
The gauge group of a principal G-bundle P over a space X is the group of G-equivariant homeomorphisms of P that cover the identity on X. To date, the study of the homotopy theory of gauge groups has been focused primarily on principal bundles whose structure groups are simply-connected, mainly due to the inherent complexity of the case of non-simply-connected structure groups. In this thesis, we carry out a systematic study of the homotopy types of gauge groups of principal bundles with two families of non-simply connected structure groups: namely, the projective unitary groups PU(n), particularly with n prime, and the complex spin groups Spinc(n). These are defined as quotients of U(n) by its centre, and of the product Spin(n) U(1) by the diagonal action, respectively. We examine the relation between the gauge groups of SU(n)- and PU(n)-bundles over the even dimensional sphere S2i, with 2 i n. As special cases, for U(5)-bundles over S4, we show that there is a rational or p-local equivalence G2;k '(p) G2;l for any prime p if, and only if, (120; k) = (120; l), while for PU(3)-bundles over S6 there is an integral equivalence G3;k ' G3;l if, and only if, (120; k) = (120; l). We also study the gauge groups of bundles over S4 with Spinc(n) as structure group and show that there is a decomposition Gk(Spinc(n)) ' S1 Gk(Spin(n)). This implies that the homotopy theory of Spinc(n)-gauge groups reduces to that of Spin(n)-gauge groups over S4. We then advance on what is known by providing a partial classification for Spin(7)- and Spin(8)-gauge groups over S4.
Dissertation
Homotopy types of \\(\\mathrm{Spin}^c(n)\\)-gauge groups over \\(S^4\\)
The gauge group of a principal \\(G\\)-bundle \\(P\\) over a space \\(X\\) is the group of \\(G\\)-equivariant homeomorphisms of \\(P\\) that cover the identity on \\(X\\). We consider the gauge groups of bundles over \\(S^4\\) with \\(\\mathrm{Spin}^c(n)\\), the complex spin group, as structure group and show how the study of their homotopy types reduces to that of \\(\\mathrm{Spin}(n)\\)-gauge groups over \\(S^4\\). We then advance on what is known by providing a partial classification for \\(\\mathrm{Spin}(7)\\)- and \\(\\mathrm{Spin}(8)\\)-gauge groups over \\(S^4\\).
Paper
Homotopy types of gauge groups of \\(\\mathrm{PU}(p)\\)-bundles over spheres
We examine the relation between the gauge groups of \\(\\mathrm{SU}(n)\\)- and \\(\\mathrm{PU}(n)\\)-bundles over \\(S^{2i}\\), with \\(2\\leq i\\leq n\\), particularly when \\(n\\) is a prime. As special cases, for \\(\\mathrm{PU}(5)\\)-bundles over \\(S^4\\), we show that there is a rational or \\(p\\)-local equivalence \\(\\mathcal{G}_{2,k}\\simeq_{(p)}\\mathcal{G}_{2,l}\\) for any prime \\(p\\) if, and only if, \\((120,k)=(120,l)\\), while for \\(\\mathrm{PU}(3)\\)-bundles over \\(S^6\\) there is an integral equivalence \\(\\mathcal{G}_{3,k}\\simeq\\mathcal{G}_{3,l}\\) if, and only if, \\((120,k)=(120,l)\\).
Paper
Ice stream motion facilitated by a shallow-deforming and accreting bed
Ice streams drain large portions of ice sheets and play a fundamental role in governing their response to atmospheric and oceanic forcing, with implications for sea-level change. The mechanisms that generate ice stream flow remain elusive. Basal sliding and/or bed deformation have been hypothesized, but ice stream beds are largely inaccessible. Here we present a comprehensive, multi-scale study of the internal structure of mega-scale glacial lineations (MSGLs) formed at the bed of a palaeo ice stream. Analyses were undertaken at macro- and microscales, using multiple techniques including X-ray tomography, thin sections and ground penetrating radar (GPR) acquisitions. Results reveal homogeneity in stratigraphy, kinematics, granulometry and petrography. The consistency of the physical and geological properties demonstrates a continuously accreting, shallow-deforming, bed and invariant basal conditions. This implies that ice stream basal motion on soft sediment beds during MSGL formation is accommodated by plastic deformation, facilitated by continuous sediment supply and an inefficient drainage system.
Ice streams are fundamental to ice sheet dynamics, but the mechanisms controlling their flow remain elusive. Here, the authors perform macro- and microscale analyses of mega-scale glacial lineations, which indicate a continuously accreting, shallow-deforming bed during ice stream flow.
Journal Article