diff --git a/thesis/chapters/Introduction.tex b/thesis/chapters/Introduction.tex index 59a4ea8..79757f8 100644 --- a/thesis/chapters/Introduction.tex +++ b/thesis/chapters/Introduction.tex @@ -1,7 +1,7 @@ \chapter*{Introduction} -Homotopy theory is the study of topological spaces and homotopy equivalences. These equivalences are weaker than isomorphism. An isomorphism is given by two maps $f : X \leftadj Y : g$, such that the both compositions are equal to identities. A homotopy equivalence weakens this by requiring the compositions to be homotopic to identities. Some properties of spaces, such as some kinds of connectedness, only depend on the homotopy type. Such properties are homotopy invariants. \todo{not happy with this yet...} +Homotopy theory is the study of topological spaces and homotopy equivalences. These equivalences are weaker than isomorphism. An isomorphism is given by two maps $f : X \leftadj Y : g$, such that the both compositions are equal to identities. A homotopy equivalence weakens this by requiring the compositions to be homotopic to identities. Some properties of spaces, such as some kinds of connectedness, only depend on the homotopy type. Such properties are homotopy invariants. Examples of homotopy invariants are homology groups $H_n(X)$ and homotopy groups $\pi_n(X)$. The latter is defined as the set of continuous maps $S^n \to X$ up to homotopy. Despite the easy definition, the groups $\pi_n(S^k)$ are very hard to calculate and much of it is even unknown as of today. diff --git a/thesis/images/A_Preserves_WCof.png b/thesis/images/A_Preserves_WCof.png deleted file mode 100644 index c869dd0..0000000 Binary files a/thesis/images/A_Preserves_WCof.png and /dev/null differ diff --git a/thesis/images/Apl_C_Quasi_Iso_LES.png b/thesis/images/Apl_C_Quasi_Iso_LES.png deleted file mode 100644 index 1a0b22c..0000000 Binary files a/thesis/images/Apl_C_Quasi_Iso_LES.png and /dev/null differ diff --git a/thesis/images/Apl_C_Quasi_Iso_Limit.png b/thesis/images/Apl_C_Quasi_Iso_Limit.png deleted file mode 100644 index 95ba94c..0000000 Binary files a/thesis/images/Apl_C_Quasi_Iso_Limit.png and /dev/null differ diff --git a/thesis/images/Apl_C_Quasi_Iso_Pushout2.png b/thesis/images/Apl_C_Quasi_Iso_Pushout2.png deleted file mode 100644 index 101a205..0000000 Binary files a/thesis/images/Apl_C_Quasi_Iso_Pushout2.png and /dev/null differ diff --git a/thesis/images/Extend_Boundary_Form.png b/thesis/images/Extend_Boundary_Form.png deleted file mode 100644 index 50e2576..0000000 Binary files a/thesis/images/Extend_Boundary_Form.png and /dev/null differ diff --git a/thesis/images/SnQ_Extension.png b/thesis/images/SnQ_Extension.png deleted file mode 100644 index e8d1ba9..0000000 Binary files a/thesis/images/SnQ_Extension.png and /dev/null differ diff --git a/thesis/images/Sullivan_Lifting.png b/thesis/images/Sullivan_Lifting.png deleted file mode 100644 index 16b3af7..0000000 Binary files a/thesis/images/Sullivan_Lifting.png and /dev/null differ diff --git a/thesis/preamble.tex b/thesis/preamble.tex index e67a878..f0a7ef6 100644 --- a/thesis/preamble.tex +++ b/thesis/preamble.tex @@ -122,25 +122,6 @@ \right|_{#2} % this is the delimiter }} -% Todos in the margin -\newcommand{\todo}[1]{ - \addcontentsline{tdo}{todo}{\protect{#1}} - $\ast$ \marginpar{\tiny $\ast$ #1} -} -% Big todos in text -\newcommand{\TODO}[1]{ - \addcontentsline{tdo}{todo}{\protect{#1}} - {\tiny $\ast$ #1} -} -% TODO item, as itemize does not work -\newcommand{\titem}[0]{\\-\qquad} -% List of todos -\makeatletter - \newcommand \listoftodos{\section*{Todo list} \@starttoc{tdo}} - \newcommand\l@todo[2]{ - \par\noindent \textit{#2}, \parbox{10cm}{#1}\par - } -\makeatother \theoremstyle{plain} \newtheorem{theorem}{Theorem}[section] diff --git a/thesis/thesis.tex b/thesis/thesis.tex index 2b55b13..1a88909 100644 --- a/thesis/thesis.tex +++ b/thesis/thesis.tex @@ -55,8 +55,6 @@ \part{Appendices} \include{chapters/Appendices} -\listoftodos - \bibliographystyle{alpha} \bibliography{references}