1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
|
%&pdfelatex
%% This is intended to be a working example of using the amsrefs
%% backrefs option in conjunction with hyperref. It works for me using
%% pdflatex [mjd,2002-01-03]. Cf testbib.tex in the hyperref distrib.
%%
%% This is pdfTeX, Version 3.14159-14h-released-20010417 (Web2C 7.3.3.1)
%% (format=pdflatex 2001.12.21)
%% Package: hyperref 2000/01/22 v6.69c Hypertext links for LaTeX
\documentclass{article}
\usepackage{times}
\usepackage[colorlinks,citecolor=red,pagebackref,hypertexnames=false]{hyperref}
\usepackage[backrefs]{amsrefs}
\newenvironment{dual}{%
\par\medskip
\trivlist\item[]%
}{%
\endtrivlist
}
\newcommand{\backup}{%
\vspace*{-\baselineskip}\vspace*{-\medskipamount}\nopagebreak
}
\newtheorem{thm}{Theorem}[section]
\providecommand{\MR}{}
\begin{document}
\title{Testing amsrefs with the hyperref package}
\author{MJD}
\maketitle
The following examples are derived from
\emph{Homology manifold bordism} by Heather Johnston and Andrew
Ranicki (Trans.\ Amer.\ Math.\ Soc.\ \textbf{352} no 11 (2000), PII: S
0002-9947(00)02630-1).
\setcounter{section}{3}
\section{Homology manifold bordism}
\begin{dual}
The results of Johnston \cite{Jo} on homology
manifolds are extended here. It is not
possible to investigate transversality by
geometric methods---as in \cite{Jo} we employ
bordism and surgery instead.
\end{dual}
%Kirby and Siebenmann \cite{KS} (III,\S 1),
\begin{dual}
The proof of transversality is indirect,
relying heavily on surgery theory\mdash see
Kirby and Siebenmann \cite{KS}*{III, \S 1},
Marin \cite{M} and Quinn \cite{Q3}. We shall
use the formulation in terms of topological
block bundles of Rourke and Sanderson
\cite{RS}.
\end{dual}
\begin{dual}
$Q$ is a codimension $q$ subspace by Theorem
4.9 of Rourke and Sanderson \cite{RS}.
(Hughes, Taylor and Williams \cite{HTW}
obtained a topological regular neighborhood
theorem for arbitrary submanifolds \dots.)
\end{dual}
%Wall \cite{Wa} (Chapter 11) obtained a
\begin{dual}
Wall \cite{Wa}*{Chapter 11} obtained a
codimension $q$ splitting obstruction \dots.
\end{dual}
\begin{dual}
\dots\ following the work of Cohen \cite{Co}
on $PL$ manifold transversality.
\end{dual}
\begin{dual}
In this case each inverse image is
automatically a $PL$ submanifold of
codimension $\sigma$ (Cohen \cite{Co}), so
there is no need to use $s$-cobordisms.
\end{dual}
%Quinn (\cite{Q2}, 1.1) proved that \dots
\begin{dual}
Quinn \cite{Q2}*{1.1} proved that \dots
\end{dual}
\begin{dual}\backup
\begin{thm}[The additive structure of
homology manifold bordism, Johnston
\cite{Jo}]
\dots
\end{thm}
\end{dual}
\begin{dual}
For $m\geq 5$ the Novikov-Wall surgery theory
for topological manifolds gives an exact
sequence (Wall \cite{Wa}*{Chapter 10}.
\end{dual}
\begin{dual}
The surgery theory of topological manifolds
was extended to homology manifolds in Quinn
\cites{Q1,Q2} and Bryant, Ferry, Mio
and Weinberger \cite{BFMW}.
\end{dual}
\begin{dual}
The 4-periodic obstruction is equivalent to
an $m$-dimensional homology manifold, by
\cite{BFMW}.
\end{dual}
\begin{dual}
Thus, the surgery exact sequence of
\cite{BFMW} does not follow Wall \cite{Wa} in
relating homology manifold structures and
normal invariants.
\end{dual}
\begin{dual}
\dots\ the canonical $TOP$ reduction
(\cite{FP}) of the Spivak normal fibration of
$M$ \dots
\end{dual}
\begin{dual}\backup
\begin{thm}[Johnston \cite{Jo}]
\dots
\end{thm}
\end{dual}
\begin{dual}
Actually \cite{Jo}*{(5.2)} is for $m\geq 7$,
but we can improve to $m\geq 6$ by a slight
variation of the proof as described below.
\end{dual}
\begin{dual}
(This type of surgery on a Poincar\'e space
is in the tradition of Lowell Jones
\cite{Jn}.)
\end{dual}
\bibliographystyle{amsxport}
\bibliography{jr}
\end{document}
|
