The Lefschetz number of self-maps of Lie groups

Duan, Hai Bao

doi:10.1090/s0002-9939-1988-0935107-8

Proc. Amer. Math. Soc.

1988

DOI: 10.1090/s0002-9939-1988-0935107-8

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The Lefschetz number of self-maps of Lie groups

Hai Bao Duan¹

Abstract: ABSTRACT. In this note we present a simple approach to the Lefschetz number for the self-maps of Lie groups. As an application it is proved that for any map /: G

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On Lefschetz series

Zhao

Gao

2011

Front. Math. China

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Let R = ⊕ ∞ i=0 R i be a connected graded commutative algebra over the field Q of rational numbers, and let f be a graded endomorphism of R. In this paper, we show that the Lefschetz series of f can be computed directly from the induced linear map Q(f ) on the Q vector space of indecomposables of R. We give an explicit algorithm to compute the Lefschetz series of f from Q(f ). The main tool we used is the graded algebra version of Gröbner basis theory. At the end of this paper, some examples and applications are given.

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On Lefschetz series

Zhao

Gao

2011

Front. Math. China

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Coincidence points of principal bundles

Gao

1992

Topology and its Applications

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Fixed-point theory for homogeneous spaces

Wong¹

1998

ajm

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Let G be a compact connected Lie group, K a closed subgroup (not necessarily connected) and M = G/K the homogeneous space of left cosets. Assume that M is orientable and p * : H n ( G ) → H n ( M ) is nonzero, where n = dim M . In this paper, we employ an equivariant version of Nielsen root theory to show that the converse of the Lefschetz fixed-point theorem holds true for all selfmaps on M . Moreover, if the Lefschetz number of a selfmap f : M → M is nonzero, then the Nielsen number of f coincides with the Reidemeister number of f , which can be computed algebraically.

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The Lefschetz number of self-maps of Lie groups

Abstract: ABSTRACT. In this note we present a simple approach to the Lefschetz number for the self-maps of Lie groups. As an application it is proved that for any map /: G

Cited by 4 publications

References 3 publications

On Lefschetz series

On Lefschetz series

Coincidence points of principal bundles

Fixed-point theory for homogeneous spaces

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