|
![]() |
|||
|
||||
OverviewThis volume contains the proceedings of the AMS Special Session on Singer-Hopf Conjecture in Geometry and Topology, held from March 18-19, 2023, at Georgia Institute of Technology, Atlanta, Georgia. It presents a multidisciplinary point of view on the Singer conjecture, the Hopf conjecture, the study on normalized Betti numbers, and several other intriguing questions on the fundamental group and cohomology of aspherical manifolds. This volume highlights many interesting research directions in the study of aspherical manifolds and covers a large collection of problems and conjectures about $L^2$-invariants of aspherical manifolds. It provides a snapshot of contemporary research in mathematics at the interface of geometry and topology, as well as algebraic geometry. The problems are presented from several distinct points of view, and the articles in this volume suggest possible generalizations and bridge a gap with closely related problems in differential geometry, complex algebraic geometry, and geometric topology. The volume can play a role in focusing the attention of the mathematical community on these fascinating problems which continue to resist the siege of geometers and topologists. It is our hope that this volume will become a valuable resource for early career mathematicians interested in these deep and important questions. Full Product DetailsAuthor: Luca F. Di Cerbo , Laurentiu G. MaximPublisher: American Mathematical Society Imprint: American Mathematical Society ISBN: 9781470474959ISBN 10: 1470474956 Pages: 170 Publication Date: 30 June 2025 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print ![]() This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsSurvey and research articles Dominik Kirstein, Christian Kremer and Wolfgang Luck, Some problems and conjectures about $L^2$-invariants Dessislava H. Kochloukova and Stefano Vidussi, with an appendix by Marco Boggi, Finiteness properties of algebraic fibers of group extensions Yongqiang Liu, $L^2$-type invariants for complex smooth quasi-projective varieties: A survey Research articles Donu Arapura, Laurentiu G. Maxim and Botong Wang, Hodge-theoretic variants of the Hopf and Singer conjectures Alexander Dranishnikov, On Lipschitz cohomology of aspherical manifolds Luca F. Di Cerbo and Michael Hull, Generalized graph manifolds, residual finiteness, and the Singer conjecture Mark Stern, $L_p$-cohomology and the geometry of $p$-harmonic formsReviewsAuthor InformationLuca F. Di Cerbo, University of Florida, Gainesville, FL. Laurentiu G. Maxim, University of Wisconsin, Madison, WI. Tab Content 6Author Website:Countries AvailableAll regions |