Converse theorem on equivariant genera

Musin, Oleg R.

doi:10.1070/rm2009v064n04abeh004635

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A Converse Theorem On Rigid Genera3

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2011

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“…(see [10,17]). So Lemma 4.1 shows that rigidity of h for C P 2 [w 0 , w 1 , w 2 ] with distinct w i yields that h is rigid for C P 2 [w 0 , w 1 , w 1 ] also.…”

Section: A Converse Theorem On Rigid Generamentioning

confidence: 99%

“…In this section we prove the main theorem which implies that a Hirzebruch genus is rigid if and only if its characteristic is the GT series. In our paper [17] we consider the case of a rigid genus h such that F H (log z) is a rational function in z. It is proved that in this case we have H = H x,y .…”

Section: A Converse Theorem On Rigid Generamentioning

confidence: 99%

“…It is proved that in this case we have H = H x,y . Surprisingly, the main line of a proof in [17] can be used also for the general case.…”

Section: A Converse Theorem On Rigid Generamentioning

confidence: 99%

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On Rigid Hirzebruch Genera

Musin¹

2011

MMJ

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The classical multiplicative (Hirzebruch) genera of manifolds have the wonderful property which is called rigidity. Rigidity of a genus h means that if a compact connected Lie group G acts on a manifold X, then the equivariant genus h G (X) is independent on G, i.e. h G (X) = h(X).In this paper we are considering the rigidity problem for stably complex manifolds. In particular, we are proving that a genus is rigid if and only if it is a generalized Todd genus.2000 MSC: 55N22, 57R77.

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“…(see [10,17]). So Lemma 4.1 shows that rigidity of h for C P 2 [w 0 , w 1 , w 2 ] with distinct w i yields that h is rigid for C P 2 [w 0 , w 1 , w 1 ] also.…”

Section: A Converse Theorem On Rigid Generamentioning

confidence: 99%

Section: A Converse Theorem On Rigid Generamentioning

confidence: 99%