Elliptische differentialoperatoren und Ganzzahligkeitssätze für charakteristische Zahlen

Ganzzahligkeitss�tze und Immersionen von Sph�renb�ndeln �ber Sph�ren

“…Beweis. Fiir dim X = n gerade und W E K°(X) ist der Satz in [7] bewiesen. Ist n gerade und W E K 1 (X) oder n ungerade und W E K°(X), dann ist die Aussage trivial.…”

“…Es seien p : X x E 2--, X und n : X x S X~X die natiirlichen Projektionen. Nach [7], § 3.1 ist ffir F E K°(X x S 1) (1) …”

Nonimmersions of low dimensional flag manifolds

“…We shall show that The methods of this paper were first used by Feder [5] to obtain nonimmersions of projective spaces CP", n odd. Mayer [9] obtains very general nonimmersion results for manifolds, but our methods give stronger results for the flag manifolds considered here. Here, the term H(BG) • H*(BH) is the ideal ofH*(BH) generatedby H(BG).…”

Twisted signatures of flag manifolds

“…It is well known that stable span(M ) = r > 0 implies divisibility conditions for the signature and also for the twisted signatures. These divisibility conditions may be deduced from a general integrality theorem, which was proved in [10] by using elliptic differential operators. For the signature these conditions are stated and proved by other methods in [1] and [6].…”

“…Z v e n g r o w s k i . When M is orientable and has dimension divisible by 4, then the signature of M may be used to determine upper bounds for stable span(M ) ( [1], [6], [10]). Actually it is possible to use twisted signatures for this purpose.…”