We study $\widetilde{H}$-cobordisms of distinguished homology handles, introduced by Kawauchi in 1976 using infinite cyclic covers. Despite the extensive development of gauge-theoretic and Floer-theoretic invariants since Kawauchi's work, none were previously known to distinguish smooth and topological $\widetilde{H}$-cobordism. In this paper, we construct asymptotic invariants of distinguished homology handles by applying real Seiberg--Witten theory to finite cyclic covers. Using these invariants, we show that the kernel of the natural map from the smooth $\widetilde{H}$-cobordism group to its topological counterpart contains a subgroup isomorphic to $\mathbb{Z}$. We also define spin versions of these groups and show that the kernel of the corresponding natural map contains a subgroup isomorphic to $\mathbb{Z}^\infty$.
We use an analogue of the Springer resolution to describe the $G$-module structure on the ring of regular functions on the universal cover $\widetilde{\mathcal{O}}$ of any nilpotent orbit for $G = SL_n$. Building on previous work on the extended Springer resolution, we construct a variety $\widetilde{\mathcal{M}}$ that...
W. Graham, S. Larson, Alberto San Miguel Malaney· 0 citations
This paper proves a generalisation of Coleman's isomorphism (between norm compatible cyclotomic units and a group of invertible power series) to various cohomology theories evaluated on proper regular $p$-adic formal schemes, for future applications to Iwasawa theory. This generalisation is an immediate consequence of...
Let $X$ carry a transversely holomorphic foliation, equivalently an elliptic involutive structure $V\subset T_{\mathbb C}X$, and let ${\mathcal O}_V$ be its sheaf of leafwise-constant, transversely holomorphic functions. We construct a finite superconnection model for the derived category of coherent ${\mathcal O}_V$-m...
Let $X$ be a connected finite-type CW-complex with fundamental group $G$. We show that the profinite completion $\widehat{G}$ determines the cohomology jump loci $\mathcal{V}^q_s(X,\mathbb{C})$ under two hypotheses: that the loci are finite unions of torsion-translated subtori, as for smooth quasi-projective varieties,...
We compare two mixed Hodge structures attached to a unipotent variation $\mathbb V$ of mixed Hodge--Tate structures on $X=\mathbb P^1\setminus{0,1,\infty}$: the cohomology of its extension by $*$ at $0$ and by $!$ at $\infty$, and the vanishing cycles at $1$. The semi-holonomy isomorphism constructed in [arXiv:2604.263...
We prove that, for every non-uniform arithmetic lattice in $\mathrm{SU}(2,1)$, its inverse images in the universal cover and in all connected finite covers are residually finite. The key new input is that every commensurability class of such lattices contains a congruence arithmetic lattice $\Gamma$ for which $$H^1_{\m...
Richard M. Hill· 0 citations
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