scholarly journals Lefschetz fixed point formula: Non-isometry case

2021 ◽  
pp. 1
Author(s):  
Zelin Yi
Keyword(s):  
Fixed Point ◽  
Lefschetz Fixed Point Formula

Local contribution to the Lefschetz fixed point formula

1993 ◽  
Vol 111 (1) ◽  
pp. 1-33 ◽  
Author(s):  
Mark Goresky ◽  
Robert MacPherson
Keyword(s):  
Fixed Point ◽  
Lefschetz Fixed Point Formula ◽  
Local Contribution

Fixed Points of Automorphisms of Compact Riemann Surfaces

1970 ◽  
Vol 22 (5) ◽  
pp. 922-932 ◽  
Author(s):  
M. J. Moore
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Riemann Surfaces ◽  
Homology Group ◽  
Group Of Automorphisms ◽  
Quartic Curve ◽  
Lefschetz Fixed Point Formula ◽  
Compact Riemann Surfaces ◽  
Klein's Quartic Curve ◽  
Fundamental Paper

In his fundamental paper [3], Hurwitz showed that the order of a group of biholomorphic transformations of a compact Riemann surface S into itself is bounded above by 84(g – 1) when S has genus g ≧ 2. This bound on the group of automorphisms (as we shall call the biholomorphic self-transformations) is attained for Klein's quartic curve of genus 3 [4] and, from this, Macbeath [7] deduced that the Hurwitz bound is attained for infinitely many values of g.After genus 3, the next smallest genus for which the bound is attained is the case g = 7. The equations of such a curve of genus 7 were determined by Macbeath [8] who also gave the equations of the transformations. The equations of these transformations were found by using the Lefschetz fixed point formula. If the number of fixed points of each element of a group of automorphisms is known, then the Lefschetz fixed point formula may be applied to deduce the character of the representation given by the group acting on the first homology group of the surface.

scholarly journals A Lefschetz fixed-point formula for certain orbifold C*-algebras

2010 ◽  
pp. 125-155 ◽  
Author(s):  
Siegfried Echterhoff ◽  
Heath Emerson ◽  
Hyun Jeong Kim
Keyword(s):  
Fixed Point ◽  
C Algebras ◽  
Lefschetz Fixed Point Formula

Holomorphic Lefschetz fixed point formula for non-compact Kähler manifolds

2008 ◽  
Vol 29 (6) ◽  
pp. 679-686 ◽  
Author(s):  
Boyong Chen ◽  
Yang Liu
Keyword(s):  
Fixed Point ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Lefschetz Fixed Point Formula

On the Lefschetz Fixed Point Formula

1967 ◽  
Vol 20 (1) ◽  
pp. 139-143 ◽  
Author(s):  
Joseph Roitberg
Keyword(s):  
Fixed Point ◽  
Lefschetz Fixed Point Formula

scholarly journals A Lefschetz Fixed Point Formula for Elliptic Quasicomplexes

2014 ◽  
Vol 78 (4) ◽  
pp. 577-587
Author(s):  
D. Wallenta
Keyword(s):  
Fixed Point ◽  
Lefschetz Fixed Point Formula

scholarly journals CATEGORICAL PROOF OF HOLOMORPHIC ATIYAH–BOTT FORMULA

2018 ◽  
Vol 19 (5) ◽  
pp. 1739-1763 ◽  
Author(s):  
Grigory Kondyrev ◽  
Artem Prikhodko
Keyword(s):  
Fixed Point ◽  
Algebraic Geometry ◽  
Commutative Diagram ◽  
Natural Morphism ◽  
Lefschetz Fixed Point Formula ◽  
Derived Algebraic Geometry

Given a $2$-commutative diagramin a symmetric monoidal $(\infty ,2)$-category $\mathscr{E}$ where $X,Y\in \mathscr{E}$ are dualizable objects and $\unicode[STIX]{x1D711}$ admits a right adjoint we construct a natural morphism $\mathsf{Tr}_{\mathscr{E}}(F_{X})\xrightarrow[{}]{~~~~~}\mathsf{Tr}_{\mathscr{E}}(F_{Y})$ between the traces of $F_{X}$ and $F_{Y}$, respectively. We then apply this formalism to the case when $\mathscr{E}$ is the $(\infty ,2)$-category of $k$-linear presentable categories which in combination of various calculations in the setting of derived algebraic geometry gives a categorical proof of the classical Atiyah–Bott formula (also known as the Holomorphic Lefschetz fixed point formula).

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