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Nielsen theory of transversal fixed point sets (with an appendix: C and C0 fixed point sets are the same, by R. E. Greene)

Helga Schirmer (1992)

Fundamenta Mathematicae

Examples exist of smooth maps on the boundary of a smooth manifold M which allow continuous extensions over M without fixed points but no such smooth extensions. Such maps are studied here in more detail. They have a minimal fixed point set when all transversally fixed maps in their homotopy class are considered. Therefore we introduce a Nielsen fixed point theory for transversally fixed maps on smooth manifolds without or with boundary, and use it to calculate the minimum number of fixed points...

Nombre de rotation, structures géométriques sur un cercle et groupe de Bott-Virasoro

Laurent Guieu (1996)

Annales de l'institut Fourier

Une classification complète des stabilisateurs coadjoints du groupe de Bott-Virasoro est obtenue par une méthode essentiellement géométrique. L’outil de base est le nombre de rotation d’un difféomorphisme du cercle. En particulier, nous mettons en évidence la présence de groupes d’isotropie non-connexes et montrons que la transformation de Miura des opérateurs de Hill peut s’interpréter comme une application moment sur l’espace des structures affines du cercle.

Non compact boundaries of complex analytic varieties in Hilbert spaces

Samuele Mongodi, Alberto Saracco (2014)

Complex Manifolds

We treat the boundary problem for complex varieties with isolated singularities, of complex dimension greater than or equal to 3, non necessarily compact, which are contained in strongly convex, open subsets of a complex Hilbert space H.We deal with the problem by cutting with a family of complex hyperplanes and applying the already known result for the compact case.

Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs

Victor V. Batyrev (1999)

Journal of the European Mathematical Society

Using non-Archimedian integration over spaces of arcs of algebraic varieties, we define stringy Euler numbers associated with arbitrary Kawamata log-terminal pairs. There is a natural Kawamata log-terminal pair corresponding to an algebraic variety V having a regular action of a finite group G . In this situation we show that the stringy Euler number of this pair coincides with the physicists’ orbifold Euler number defined by the Dixon-Harvey-Vafa-Witten formula. As an application, we prove a conjecture...

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