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On Sp(2) and Sp(2) · Sp(1) structures in 8-dimensional vector bundles.

Martin Cadek, Jirí Vanzura (1997)

Publicacions Matemàtiques

Let ξ be an oriented 8-dimensional vector bundle. We prove that the structure group SO(8) of ξ can be reduced to Sp(2) or Sp(2) · Sp(1) if and only if the vector bundle associated to ξ via a certain outer automorphism of the group Spin(8) has 3 linearly independent sections or contains a 3-dimensional subbundle. Necessary and sufficient conditions for the existence of an Sp(2)- structure in ξ over a closed connected spin manifold of dimension 8 are also given in terms of characteristic classes.

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 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 topological invariants of vector bundles

Zbigniew Szafraniec (1992)

Annales Polonici Mathematici

Let E → W be an oriented vector bundle, and let X(E) denote the Euler number of E. The paper shows how to calculate X(E) in terms of equations which describe E and W.

Currently displaying 201 – 220 of 346