  In this work, we study the deformation theory of $\cE_n$-rings and the
$\cE_n$ analogue of the tangent complex, or topological Andr\'e-Quillen
cohomology. We prove a generalization of a conjecture of Kontsevich, that there
is a fiber sequence $A[n-1] \ra T_A\ra \hh^*_{\cE_{n}}(A)[n]$, relating the
$\cE_n$-tangent complex and $\cE_n$-Hochschild cohomology of an $\cE_n$-ring
$A$. We give two proofs: The first is direct, reducing the problem to certain
stable splittings of configuration spaces of punctured Euclidean spaces; the
second is more conceptual, where we identify the sequence as the Lie algebras
of a fiber sequence of derived algebraic groups, $B^{n-1}A^\times\ra \Aut_A\ra
\Aut_{\fB^nA}$. Here $\fB^nA$ is an enriched $(\oo,n)$-category constructed
from $A$, and $\cE_n$-Hochschild cohomology is realized as the infinitesimal
automorphisms of $\fB^nA$. These groups are associated to moduli problems in
$\cE_{n+1}$-geometry, a {\it less} commutative form of derived algebraic
geometry, in the sense of To\"en-Vezzosi and Lurie. Applying techniques of
Koszul duality, this sequence consequently attains a nonunital
$\cE_{n+1}$-algebra structure; in particular, the shifted tangent complex
$T_A[-n]$ is a nonunital $\cE_{n+1}$-algebra. The $\cE_{n+1}$-algebra structure
of this sequence extends the previously known $\cE_{n+1}$-algebra structure on
$\hh^*_{\cE_{n}}(A)$, given in the higher Deligne conjecture. In order to
establish this moduli-theoretic interpretation, we make extensive use of
factorization homology, a homology theory for framed $n$-manifolds with
coefficients given by $\cE_n$-algebras, constructed as a topological analogue
of Beilinson-Drinfeld's chiral homology. We give a separate exposition of this
theory, developing the necessary results used in our proofs. This work is an
elaboration of a chapter of the author's 2008 PhD thesis, \cite{thez}.
