  In Part I, we study a special case of the unweighted Tree Augmentation
Problem (TAP) via the Lasserre (Sum of Squares) system. In the special case, we
forbid so-called stems; these are a particular type of subtree configuration.
For stemless TAP, we prove that the integrality ratio of an SDP relaxation (the
Lasserre tightening of an LP relaxation) is $\leq \frac{3}{2}+\epsilon$, where
$\epsilon>0$ can be any small constant. We obtain this result by designing a
polynomial-time algorithm for stemless TAP that achieves an approximation
guarantee of ($\frac32+\epsilon$) relative to the SDP relaxation. The algorithm
is combinatorial and does not solve the SDP relaxation, but our analysis relies
on the SDP relaxation.
  We generalize the combinatorial analysis of integral solutions from the
previous literature to fractional solutions by identifying some properties of
fractional solutions of the Lasserre system via the decomposition result of
Karlin, Mathieu and Nguyen (IPCO 2011).
  Also, we present an example of stemless TAP such that the approximation
guarantee of $\frac32$ is tight for the algorithm.
  In Part II of this paper, we extend the methods of Part I to prove the same
results relative to the same SDP relaxation for TAP.
