Overview

This 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 Details

Author:   Luca F. Di Cerbo ,  Laurentiu G. Maxim
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
ISBN:  

9781470474959

ISBN 10:   1470474956
Pages:   170
Publication Date:   30 June 2025
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Survey 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 forms

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Author Information

Luca F. Di Cerbo, University of Florida, Gainesville, FL. Laurentiu G. Maxim, University of Wisconsin, Madison, WI.

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