Given a family of groups admitting a braided monoidal structure (satisfying mild
assumptions) we construct a family of spaces on which the groups act and whose …

Let C n (M) be the configuration space of n distinct ordered points in M. We prove that if M is
any connected orientable manifold (closed or open), the homology groups H i (C n (M); ℚ) …

We consider the limiting behavior of discriminants, by which we mean informally the locus in
some parameter space of some type of object where the objects have certain singularities …

Using factorization homology, we realize the rational homology of the unordered
configuration spaces of an arbitrary manifold M, possibly with boundary, as the homology of …

An FI-module V over a commutative ring K encodes a sequence (V n) n≥ 0 of
representations of the symmetric groups (G n) n≥ 0 over K. We show that for a" finitely …

arXiv:1608.07490v2 [math.AT] 24 Jul 2017 Page 1 arXiv:1608.07490v2 [math.AT] 24 Jul 2017
BETTI NUMBERS OF CONFIGURATION SPACES OF SURFACES GABRIEL C …

Using the language of twisted skew-commutative algebras, we define secondary
representation stability, a stability pattern in the unstable homology of spaces that are …

Given a graded E 1–module over an E 2–algebra in spaces, we construct an augmented
semi-simplicial space up to higher coherent homotopy over it, called its canonical resolution …

Representation stability is a phenomenon whereby the structure of certain sequences $ X_n
$ of spaces can be seen to stabilize when viewed through the lens of representation theory …

Motivated by analogies with basic density theorems in analytic number theory, we introduce
a notion (and variations) of the homological density of one space in another. We use Weil's …