“Kervaire semi-characteristic”的意思、由来-开放百科全书

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Kervaire semi-characteristic

释义

References
Notes

In mathematics, the Kervaire semi-characteristic, introduced by {{harvs|txt|last=Kervaire|authorlink=Michel Kervaire|year=1956}}, is an invariant of manifolds M of dimension 4n+1 taking values in Z/2Z, given by

k(M) =

{{harvtxt|Atiyah|Singer|1971}} showed that it is given by the index of a skew-adjoint elliptic operator.

Assuming M is oriented, the Atiyah vanishing theorem states that if M has two linearly independent vector fields, then k(M) = 0.^[1]

References

{{citation|last1= Atiyah|first1= Michael F. |author1-link=Michael Atiyah|last2=Singer|first2= Isadore M. |author2-link=Isadore Singer|title=The Index of Elliptic Operators V|journal=Annals of Mathematics |series=Second Series|volume= 93|issue= 1|year= 1971|pages= 139–149|doi= 10.2307/1970757|publisher= The Annals of Mathematics, Vol. 93, No. 1 |jstor=1970757}}
{{Citation | last1=Kervaire | first1=Michel | title=Courbure intégrale généralisée et homotopie | doi=10.1007/BF01342961 |mr=0086302 | year=1956 | journal=Mathematische Annalen | issn=0025-5831 | volume=131 | pages=219–252}}

Notes

1. ^{{cite book|last=Weiping|first=Zhang|title=Lectures On Chern-weil Theory And Witten Deformations|url=https://books.google.com/books?id=8OfUCgAAQBAJ&pg=PA105|accessdate=6 July 2018|date=2001-09-21|publisher=World Scientific|isbn=9789814490627|page=105}}

1 : Differential topology

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