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A new invariant and parametric connected sum of embeddings

A. Skopenkov (2007)

Fundamenta Mathematicae

We define an isotopy invariant of embeddings N → ℝ m of manifolds into Euclidean space. This invariant together with the α-invariant of Haefliger-Wu is complete in the dimension range where the α-invariant could be incomplete. We also define parametric connected sum of certain embeddings (analogous to surgery). This allows us to obtain new completeness results for the α-invariant and the following estimation of isotopy classes of embeddings. In the piecewise-linear category, for a (3n-2m+2)-connected...

A note on characteristic classes

Jianwei Zhou (2006)

Czechoslovak Mathematical Journal

This paper studies the relationship between the sections and the Chern or Pontrjagin classes of a vector bundle by the theory of connection. Our results are natural generalizations of the Gauss-Bonnet Theorem.

A note on generalized flag structures

Tomasz Rybicki (1998)

Annales Polonici Mathematici

Generalized flag structures occur naturally in modern geometry. By extending Stefan's well-known statement on generalized foliations we show that such structures admit distinguished charts. Several examples are included.

A note on the cohomology ring of the oriented Grassmann manifolds G ˜ n , 4

Tomáš Rusin (2019)

Archivum Mathematicum

We use known results on the characteristic rank of the canonical 4 –plane bundle over the oriented Grassmann manifold G ˜ n , 4 to compute the generators of the ℤ 2 –cohomology groups H j ( G ˜ n , 4 ) for n = 8 , 9 , 10 , 11 . Drawing from the similarities of these examples with the general description of the cohomology rings of G ˜ n , 3 we conjecture some predictions.

A Note on the Rational Cuspidal Curves

Piotr Nayar, Barbara Pilat (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

In this short note we give an elementary combinatorial argument, showing that the conjecture of J. Fernández de Bobadilla, I. Luengo-Velasco, A. Melle-Hernández and A. Némethi [Proc. London Math. Soc. 92 (2006), 99-138, Conjecture 1] follows from Theorem 5.4 of Brodzik and Livingston [arXiv:1304.1062] in the case of rational cuspidal curves with two critical points.

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