117 citations · 228 across the 28 of their papers we have counts for
31 papers
Families of singular algebraic varieties that are rationally elliptic spaces
A. Libgober
We discuss families of hypersurfaces with isolated singularities in projective space with the property that the sum of the ranks of the rational homotopy and the homology groups is…
CAT(0) geometry of complex curve complements and families
Corey Bregman, Anatoly Libgober, Kejia Zhu
Motivated by the question of whether braid groups are CAT(0), we investigate the CAT(0) behavior of fundamental groups of plane curve complements and certain universal families. If…
Instanton Floer homology and Milnor Fibers
Kyoung-Seog Lee, Anatoly Libgober, Nikolai Saveliev
In the early days of the Floer theory, Atiyah asked if there is a Milnor fiber description of the Floer homology of the links of singularities. We answer this question for the Brie…
Braid monodromy and Alexander polynomials of real plane curves
A. Libgober
We describe symmetries of the braid monodromy decomposition for a class of plane curves defined over reals including the real curves with no real points and proving new divisibilit…
Self-products of rationally elliptic spaces and inequalities between the ranks of homotopy and homology groups
Anatoly Libgober, Shoji Yokura
We give a survey on recent results on inequalities between the ranks of homotopy and cohomology groups (resp., graded components of mixed Hodge structures on these groups) of ratio…
Ranks of homotopy and cohomology groups for rationally elliptic spaces and algebraic varieties
Anatoly Libgober, Shoji Yokura
We discuss inequalities between the values of \emph{homotopical and cohomological Poincaré polynomials} of the self-products of rationally elliptic spaces. For rationally elliptic…