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On Köthe sequence spaces and linear logic
 Mathematical Structures in Computer Science
, 2001
"... We present a category of locally convex topological vector spaces which is a model of propositional classical linear logic, based on the standard concept of Kothe sequence spaces. In this setting, the spaces interpreting the exponential have a quite simple structure of commutative Hopf algebra. The ..."
Abstract

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We present a category of locally convex topological vector spaces which is a model of propositional classical linear logic, based on the standard concept of Kothe sequence spaces. In this setting, the spaces interpreting the exponential have a quite simple structure of commutative Hopf algebra. The coKleisli category of this linear category is a cartesian closed category of entire mappings. This work provides a simple setting where typed calculus and dierential calculus can be combined; we give a few examples of computations. 1
Mathematik und Naturwissenschaften
"... The present thesis approaches the loop space of a Riemannian 3manifold (M, 〈, 〉) from a geometric point of view. Loops are immersed circles represented by immersions γ: S 1 → M modulo reparametrizations. In this setup, the loop space M appears as the base of a principal bundle π: Imm(S 1, M) → Imm ..."
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The present thesis approaches the loop space of a Riemannian 3manifold (M, 〈, 〉) from a geometric point of view. Loops are immersed circles represented by immersions γ: S 1 → M modulo reparametrizations. In this setup, the loop space M appears as the base of a principal bundle π: Imm(S 1, M) → Imm(S 1, M)/Di (S 1) =: M. The tangent space at γ may be identi ed with the space Γ(⊥γ) of smooth sections of the loop's normal bundle. A ne connections on M are constructed. Firstly, the LeviCivita connection ∇LC belonging to the Kähler structure (J, 〈〈, 〉〉), where 〈〈, 〉 〉 denotes the L2 product of normal elds and the almost complex structure J is given by 90 ◦ left rotation in the normal bundle. Its curvature and topological properties of the distance function induced by 〈〈, 〉 〉 are analyzed. Secondly, a previously unknown complex linear connection ∇C on M is described, which depends only on the conformal class of (M, 〈, 〉). The introduction of the conformally invariant harmonic mean