skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


This content will become publicly available on April 1, 2026

Title: Wall's Stable Realization for Diffeomorphisms of Definite 4-manifolds
ABSTRACT. Let X be a smooth simply connected closed 4- manifold with definite intersection form. We show that any automorphism of the intersection form of X is realized by a dif- feomorphism of X#(S2×S2). This extends and completes Wall’s foundational result from 1964.  more » « less
Award ID(s):
1952790
PAR ID:
10599416
Author(s) / Creator(s):
;
Editor(s):
Demeter, Ciprian; Jolly, Michael; Judge, Chris; Le, Nam; Levenberg, Norm; Mandell, Michael; Pilgrim, Kevin; Sternberg, Peter; Strauch, Matthias; Wang, Shouhong
Publisher / Repository:
Indiana University
Date Published:
Journal Name:
Indiana University mathematics journal
Volume:
74
Issue:
1
ISSN:
1943-5266
Page Range / eLocation ID:
225-231
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. We extend results of Looijenga--Lunts and Verbitsky and show that the total Lie algebra $$\mathfrak g$$ for the intersection cohomology of a primitive symplectic variety $$X$$ with isolated singularities is isomorphic to $$\mathfrak g \cong \mathfrak{so}\left(\left(IH^2(X, \mathbb Q), Q_X\right)\oplus \mathfrak h\right),$$ where $$Q_X$$ is the intersection Beauville--Bogomolov--Fujiki form and $$\mathfrak h$$ is a hyperbolic plane. This gives a new, algebraic proof for irreducible holomorphic symplectic manifolds which does not rely on the hyperk\"ahler metric. Along the way, we study the structure of $$IH^*(X, \mathbb Q)$$ as a $$\mathfrak{g}$$-representation -- with particular emphasis on the Verbitsky component, multidimensional Kuga--Satake constructions, and Mumford--Tate algebras -- and give some immediate applications concerning the $P = W$ conjecture for primitive symplectic varieties. Comment: 41 pages; Final journal version; new subsection on LLV algebra for symplectic orbifolds 
    more » « less
  2. An aqueous-based metal ion crosslinking approach for assembly of metal chalcogenide nanoparticles (NPs) into robust gels is reported. Short chalcogenide ligands (S2−) undergo crosslinking with metal salts (Sn4+) to form a gel [NP/S2−/Sn4+]n (NP = PbTe, PbS, CdS, CdSe). The corresponding aerogel networks retain the crystallinity and quantum confinement effects of the native building blocks while achieving excellent porosity [Brunauer–Emmett–Teller (BET) surface areas of 160–238 m2/g]. Treatment of sulfide-capped PbTe nanoparticles with an excess of Sn4+ leads to ion exchange and formation of an amorphous “SnTe” gel. 
    more » « less
  3. Galaxy clusters form from the infall of dark and baryonic matter at the intersection of cosmic filaments. Most of the baryons are in the form of a hot, magnetized, intracluster plasma detected through its X-ray thermal bremsstrahlung emission. This plasma is tightly coupled to a second, cosmic ray plasma, detected through its synchrotron radio emission. Together, the properties of these plasmas encode the history of the cluster's formation and provide a snapshot of the ongoing cluster evolution. This article provides an overview for the more general astrophysical and space plasma community of the dynamical processes revealed by the diffuse plasma emissions. 
    more » « less
  4. Three new NaBa2M3Q3(Q2) (M = Ag, Cu; Q = S, Se) chalcogenides were prepared using solid-state methods and structurally characterized using single-crystal X-ray diffraction. NaBa2Ag3Se3(Se2) and NaBa2Cu3Se3(Se2) crystallize in the monoclinic C2/m space group and have a two-dimensional structure composed of edge-sharing MSe4/4 tetrahedra separated by Na+ and Ba2+ cations, along with (Se2)2- dimers at the center of the spacings between [M3Se3]3- slabs. NaBa2Ag3S3(S2) adopts a related structure with the C2/m space group but has additional, crystallographically distinct Ag atoms in the [Ag3S3]3- layer that are linearly coordinated. NaBa2Ag3Se3(Se2) and NaBa2Ag3S3(S2) have indirect band gaps measured to be 1.2 eV and 1.9 eV, respectively, which is supported by band structures calculated using density functional theory. Mixed- anion NaBa2Cu3Se5-xSx compositions were prepared to probe for the presence of anion ordering and heteronuclear (S-Se)2- dimers. Structural analyses of the sulfoselenides indicate selenium preferentially occupies the Q-Q dimer sites, while Raman spectroscopy reveals a mixture of (S2), (Se2), and heteronuclear (S-Se) units in the sulfur-rich products. The local ordering of the chalcogens is rationalized using simple bonding concepts and adds to a growing framework for understanding ordering phenomena in mixed-anion systems. 
    more » « less
  5. The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) spike protein binds the receptor angiotensin converting enzyme 2 (ACE2) and drives virus-host membrane fusion through refolding of its S2 domain. Whereas the S1 domain contains high sequence variability, the S2 domain is conserved and is a promising pan-betacoronavirus vaccine target. We applied cryo–electron tomography to capture intermediates of S2 refolding and understand inhibition by antibodies to the S2 stem-helix. Subtomogram averaging revealed ACE2 dimers cross-linking spikes before transitioning into S2 intermediates, which were captured at various stages of refolding. Pan-betacoronavirus neutralizing antibodies targeting the S2 stem-helix bound to and inhibited refolding of spike prehairpin intermediates. Combined with molecular dynamics simulations, these structures elucidate the process of SARS-CoV-2 entry and reveal how pan-betacoronavirus S2-targeting antibodies neutralize infectivity by arresting prehairpin intermediates. 
    more » « less