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On the linearization theorem for proper Lie groupoids

Marius Crainic, Ivan Struchiner (2013)

Annales scientifiques de l'École Normale Supérieure

We revisit the linearization theorems for proper Lie groupoids around general orbits (statements and proofs). In the fixed point case (known as Zung’s theorem) we give a shorter and more geometric proof, based on a Moser deformation argument. The passage to general orbits (Weinstein) is given a more conceptual interpretation: as a manifestation of Morita invariance. We also clarify the precise statements of the Linearization Theorem (there has been some confusion on this, which has propagated throughout...

On the local isometric imbedding problem of 2-dimensional Riemannian manifolds in Euclidean space

P. A. Bozonis (1969)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

On the Milnor fibrations of weighted homogeneous polynomials

Alexandru Dimca (1990)

Compositio Mathematica

On the Morse Complex.

Xiao-Wei Peng (1984)

Mathematische Zeitschrift

On the Nature of Thin Complements of Complete Kähler Metrics.

Klas Diederich, John Eric Fornaess (1984)

Mathematische Annalen

On the non-invariance of span and immersion co-dimension for manifolds

Diarmuid J. Crowley, Peter D. Zvengrowski (2008)

Archivum Mathematicum

In this note we give examples in every dimension $m \geq 9$ of piecewise linearly homeomorphic, closed, connected, smooth $m$ -manifolds which admit two smoothness structures with differing spans, stable spans, and immersion co-dimensions. In dimension $15$ the examples include the total spaces of certain $7$ -sphere bundles over $S^{8}$ . The construction of such manifolds is based on the topological variance of the second Pontrjagin class: a fact which goes back to Milnor and which was used by Roitberg to give examples...

On the Novikov complex for rational Morse forms

Andrei Vladimirovich Pazhitnov (1995)

Annales de la Faculté des sciences de Toulouse : Mathématiques

On the number of components of the symplectic representatives of the canonical class

Stefano Vidussi (2007)

Journal of the European Mathematical Society

We show that there exists a family of simply connected, symplectic 4-manifolds such that the (Poincaré dual of the) canonical class admits both connected and disconnected symplectic representatives. This answers a question raised by Fintushel and Stern.