From be5b856034470ef879ae1bf4d0a76bb9aedc623f Mon Sep 17 00:00:00 2001 From: Robin Cruz Date: Tue, 26 Apr 2016 11:26:09 -0600 Subject: [PATCH] Fixed two typos on page 3 and 4 --- rcruz.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/rcruz.tex b/rcruz.tex index fbd7d3e..ae84a59 100644 --- a/rcruz.tex +++ b/rcruz.tex @@ -1,5 +1,5 @@ Note that in view of \eqref{mappingconelift} the lift of classes -of $H_2({X}, \partial {X})$ or $H^2(X)$ is the sum of two in general +of $H^2({X}, \partial {X})$ or $H^2(X)$ is the sum of two in general non-holomorphic modular forms (see below). In \cite{FMres} we systematically study for $\Orth(p,q)$ the @@ -25,10 +25,10 @@ \subsubsection*{Linking numbers in $3$-manifolds of type Sol} \[ \Lk(a,b) = A \cdot b \] -of (rational) chains in $M$. Here $A$ is a $2$-chain in $M$ with boundary $a$. We show +of (rational) chains in $M$. Here $A$ is a $2$-chain in $M$ with boundary $a$. We show \begin{theorem}\label{FM-linking} (Theorem~\ref{xi'-integralP}) -Let $c$ be \bf{homologically} trivial $1$-cycle in $\partial \overline{X}$ which +Let $c$ be \textbf{homologically} trivial $1$-cycle in $\partial \overline{X}$ which is disjoint from the torus fibers containing components of $\partial C_n$. Then the holomorphic part of the weight $2$ non-holomorphic modular form $\int_c \theta_{\phi_1^W}$ is given by the generating