70 citations · 93 across the 11 of their papers we have counts for
17 papers
On exponential groups and Maurer-Cartan spaces
Alexander Berglund
The purpose of this note is to give a concise account of some fundamental properties of the exponential group and the Maurer-Cartan space associated to a complete dg Lie algebra. I…
Algebraic models for classifying spaces of fibrations
Alexander Berglund, Tomáš Zeman
We prove new structural results for the rational homotopy type of the classifying space of fibrations with fiber a simply connected finite CW-complex .…
Characteristic classes for families of bundles
Alexander Berglund
The generalized Miller-Morita-Mumford classes of a manifold bundle with fiber depend only on the underlying -fibration, meaning the family of vector bundles formed by the…
A dg Lie model for relative homotopy automorphisms
Alexander Berglund, Bashar Saleh
We construct a dg Lie model for the universal cover of the classifying space of the grouplike monoid of homotopy automorphisms of a space that fix a given subspace.
Koszul A-infinity algebras and free loop space homology
Alexander Berglund, Kaj Börjeson
We introduce a notion of Koszul A-infinity algebra that generalizes Priddy's notion of a Koszul algebra and we use it to construct small A-infinity algebra models for Hochschild co…
Hirzebruch L-polynomials and multiple zeta values
Alexander Berglund, Jonas Bergström
We express the coefficients of the Hirzebruch L-polynomials in terms of certain alternating multiple zeta values. In particular, we show that every monomial in the Pontryagin class…
Rational models for automorphisms of fiber bundles
Alexander Berglund
Given a fiber bundle, we construct a differential graded Lie algebra model for the classifying space of the monoid of homotopy equivalences of the base covered by a fiberwise isomo…
Free Loop Space Homology of Highly Connected Manifolds
Alexander Berglund, Kaj Börjeson
We calculate the homology of the free loop space of (n-1)-connected closed manifolds of dimension at most 3n-2 (n > 1), with the Chas-Sullivan loop product and loop bracket. Over a…
Homotopic Hopf-Galois extensions revisited
Alexander Berglund, Kathryn Hess
In this article we revisit the theory of homotopic Hopf-Galois extensions introduced in arXiv:0902.3393v2 [math.AT], in light of the homotopical Morita theory of comodules establis…
Homotopical Morita theory for corings
Alexander Berglund, Kathryn Hess
A coring (A,C) consists of an algebra A and a coalgebra C in the monoidal category of A-bimodules. Corings and their comodules arise naturally in the study of Hopf-Galois extension…
Rational homotopy theory of automorphisms of manifolds
Alexander Berglund, Ib Madsen
We study the rational homotopy types of classifying spaces of automorphism groups of smooth simply connected manifolds of dimension at least five. We give dg Lie algebra models for…
Homological stability of diffeomorphism groups
Alexander Berglund, Ib Madsen
In this paper we prove a stability theorem for block diffeomorphisms of 2d-dimensional manifolds that are connected sums of S^d x S^d. Combining this with a recent theorem of S. Ga…
Rational homotopy theory of mapping spaces via Lie theory for L-infinity algebras
Alexander Berglund
We calculate the higher homotopy groups of the Deligne-Getzler infinity-groupoid associated to a nilpotent L-infinity algebra. As an application, we present a new approach to the r…
Koszul spaces
Alexander Berglund
We prove that a nilpotent space is both formal and coformal if and only if it is rationally homotopy equivalent to the derived spatial realization of a graded commutative Koszul al…
Homological perturbation theory for algebras over operads
Alexander Berglund
We extend homological perturbation theory to encompass algebraic structures governed by operads and cooperads. The main difficulty is to find a suitable notion of algebra homotopy…
Shellability and the strong gcd-condition
Alexander Berglund
Shellability is a well-known combinatorial criterion for verifying that a simplicial complex is Cohen-Macaulay. Another notion familiar to commutative algebraists, but which has no…
Poincare' series of monomial rings
Alexander Berglund
Let R be the quotient of a polynomial ring over a field k by an ideal generated by monomials. We derive a formula for the multigraded Poincare' series of R, i.e., the generating fu…