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HILBERT STRATIFOLDS AND A QUILLEN TYPE GEOMETRIC DESCRIPTION OF COHOMOLOGY FOR HILBERT MANIFOLDS
Forum of Mathematics, Sigma, 2018 In this paper we use tools from differential topology to give a geometric description of cohomology for Hilbert manifolds. Our model is Quillen’s geometric description of cobordism groups for finite-dimensional smooth manifolds [Quillen, ‘Elementary ...
MATTHIAS KRECK, HAGGAI TENE
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Infinitely many M2-instanton corrections to M-theory on G 2-manifolds
Journal of High Energy Physics, 2018 We consider the non-perturbative superpotential for a class of four-dimensional N=1 $$ \mathcal{N}=1 $$ vacua obtained from M-theory on seven-manifolds with holonomy G 2. The class of G 2-holonomy manifolds we consider are so-called twisted connected sum
Andreas P. Braun +5 more
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Characterizing the topology of infinite-dimensional 𝜎-compact manifolds [PDF]
Proceedings of the American Mathematical Society, 1984 A metric space ( X , d ) (X,d)
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The topology of finite and infinite-dimensional Stiefel manifolds
, 2023 Stiefel manifolds arise naturally as spaces of injective operators and as total spaces of principal bundles over Grassmannians. While their finite-dimensional topology is governed by Bott periodicity, the infinite-dimensional theory exhibits a striking collapse phenomenon stemming from Kuiper's contractibility theorem.
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On topologies of triangulated infinite-dimensional manifolds
Journal of the Mathematical Society of Japan, 1987 Let R n be considered as the subset of the countable infinite product \(R^{\omega}\) of the real line R. The set \(\cup_{n\in N}R\) n admits two different topologies. One is the weak topology with respect to the tower \(\{\) R \(n\}_{n\in N}\) and the space with this topology is denoted by \(R^{\infty}\). Another is the relative topology inherited from
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Free topological inverse semigroups as infinite-dimensional manifolds
, 2008 Let $K$ be a complete quasivariety of topological inverse Clifford semigroups, containing all topological semilattices. It is shown that the free topological inverse semigroup $F(X,K)$ of $X$ in the class $K$ is an $R^\infty$-manifold if and only if $X$ has no isolated points and $F(X,K)$ is a retract of an $R^\infty$-manifold. We derive from this that
Banakh, T., Hryniv, O.
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Topological Aspects of the Equivariant Index Theory of Infinite-Dimensional LT-Manifolds
, 2020 Let $T$ be the circle group and let $LT$ be its loop group. We formulate and investigate several topological aspects of the $LT$-equivariant index theory for proper $LT$-spaces, where proper $LT$-spaces are infinite-dimensional manifolds equipped with "proper cocompact" $LT$-actions.
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Topological classification of infinite dimensional manifolds by homotopy type [PDF]
Bulletin of the American Mathematical Society, 1970 Henderson, David W., Schori, R.
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Dimensional reduction is a generic consequence of dissipation in nonlinear evolution equations, often leading to attractor collapse and the loss of dynamical richness. To counteract this, we introduce a geometric framework for Covariant Multi-Scale Negative Coupling Systems (C-MNCS), formulated intrinsically on smooth Riemannian manifolds for a broad ...
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Topological manifolds modeled on infinite-dimensional spaces
Topological manifolds modeled on infinite-dimensional spaces2007 【要旨】
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