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Geometry of crystallographic groups
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Description
Rating
Title
Geometry
of
crystallographic
groups
Creator
Szczepanski, Andrzej.
Contributors
World Scientific (Firm)
DescriptionAbstract
Crystallographic
groups
are
groups
which
act
in a
nice
way
and
via
isometries
on
some
ndimensional
Euclidean
space
. They
got
their
name
,
because
in
three
dimensions
they
occur
as the
symmetry
groups
of a
crystal
(which
we
imagine
to
extend
to
infinity
in
all
directions)
. The
book
is
divided
into
two
parts
. In the
first
part
, the
basic
theory
of
crystallographic
groups
is
developed
from the
very
beginning
,
while
in the
second
part
,
more
advanced
and
more
recent
topics
are
discussed
.
So
the
first
part
of the
book
should be
usable
as a
textbook
,
while
the
second
part
is
more
interesting
to
researchers
in the
field
. There are
short
introductions
to the
theme
before
every
chapter
. At the
end
of this
book
is
a
list
of
conjectures
and
open
problems
.
Moreover
there are
three
appendices
. The
last
one
gives
an
example
of the
torsion
free
crystallographic
group
with a
trivial
center
and a
trivial
outer
automorphism
group
. This
volume
omits
topics
about
generalization
of
crystallographic
groups
to
nilpotent
or
solvable
world
and
classical
crystallography
.
We
want
to
emphasize
that
most
theorems
and
facts
presented
in the
second
part
are from the
last
two
decades
. This
is
after
the
book
of
L
Charlap
"
Bieberbach
groups
and
flat
manifolds
" was
published
.
DescriptionTable Of Contents
1
.
Definitions
.
1.1
.
Exercises

2
.
Bieberbach
Theorems
.
2.1
. The
first
Bieberbach
Theorem
.
2.2
.
Proof
of the
second
Bieberbach
Theorem
.
2.3
.
Proof
of the
third
Bieberbach
Theorem
.
2.4
.
Exercises

3
.
Classification
methods
.
3.1
.
Three
methods
of
classification
.
3.2
.
Classification
in
dimension
two
.
3.3
.
Platycosms
.
3.4
.
Exercises

4
.
Flat
manifolds
with
b[symbol]
=
0.
4.1
.
Examples
of
(non)primitive
groups
.
4.2
.
Minimal
dimension
.
4.3
.
Exercises

5
.
Outer
automorphism
groups
.
5.1
.
Some
representation
theory
and
9diagrams
.
5.2
.
Infinity
of
outer
automorphism
group
.
5.3
.
R[symbol]groups
.
5.4
.
Exercises

6
.
Spin
structures
and
Dirac
operator
.
6.1
.
Spin(n)
group
.
6.2
.
Vector
bundles
.
6.3
.
Spin
structure
.
6.4
. The
Dirac
operator
.
6.5
.
Exercises

7
.
Flat
manifolds
with
complex
structures
.
7.1
.
Kahler
flat
manifolds
in
low
dimensions
.
7.2
. The
Hodge
diamond
for
Kahler
flat
manifolds
.
7.3
.
Exercises

8
.
Crystallographic
groups
as
isometries
of
H[symbol]
.
8.1
.
Hyperbolic
space
H[symbol]
.
8.2
.
Exercises

9
.
HantzscheWendt
groups
.
9.1
.
Definitions
.
9.2
.
Nonoriented
GHW
groups
.
9.3
.
Graph
connecting
GHW
manifolds
.
9.4
.
Abelianization
of
HW
group
.
9.5
.
Relation
with
Fibonacci
groups
.
9.6
. An
invariant
of
GHW
.
9.7
.
Complex
HantzscheWendt
manifolds
.
9.8
.
Exercises

10
.
Open
problems
.
10.1
. The
classification
problems
.
10.2
. The
Anosov
relation
for
flat
manifolds
.
10.3
.
Generalized
HantzscheWendt
flat
manifolds
.
10.4
.
Flat
manifolds
and
other
geometries
.
10.5
. The
Auslander
conjecture
.
Publisher
World Scientific Pub. Co.
Subject
Crystallography, Mathematical.
Symmetry groups.
Identifier
9789814412261
(electronic
bk.)
;
9789814412254
(hbk.
:
alk.
paper)
;
http://www.worldscientific.com/worldscibooks/10.1142/8519#t=toc
Language
eng
Type
Electronic books.
FormatExtent
xi, 195 p. : ill.
Date
c2012
.
RelationIs Part Of
Algebra and discrete mathematics
v. 4
OCLC number
874498395
CONTENTdm number
529
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