scholarly journals A fixed point formula of Lefschetz type in Arakelov geometry II: A residue formula

2002 ◽  
Vol 52 (1) ◽  
pp. 81-103 ◽  
Author(s):  
Kai Köhler ◽  
Damien Roessler
Keyword(s):  
Fixed Point ◽  
Residue Formula ◽  
Lefschetz Type ◽  
Arakelov Geometry

scholarly journals A fixed point formula of Lefschetz type in Arakelov geometry I: statement and proof

2001 ◽  
Vol 145 (2) ◽  
pp. 333-396 ◽  
Author(s):  
Kai Köhler ◽  
Damian Roessler
Keyword(s):  
Fixed Point ◽  
Lefschetz Type ◽  
Arakelov Geometry

scholarly journals A Lefschetz-type fixed point theorem

1975 ◽  
Vol 88 (2) ◽  
pp. 103-115 ◽  
Author(s):  
L. Górniewicz
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Lefschetz Type

Local index theory for operators associated with Lie groupoid actions

2020 ◽  
pp. 1-45
Author(s):  
Denis Perrot
Keyword(s):  
Fixed Point ◽  
Index Theory ◽  
Cyclic Cohomology ◽  
Lie Groupoids ◽  
Fixed Point Set ◽  
Local Index ◽  
Lie Groupoid ◽  
Residue Formula ◽  
Isometric Actions ◽  
Point Set

We develop a local index theory for a class of operators associated with non-proper and non-isometric actions of Lie groupoids on smooth submersions. Such actions imply the existence of a short exact sequence of algebras, relating these operators to their non-commutative symbol. We then compute the connecting map induced by this extension on periodic cyclic cohomology. When cyclic cohomology is localized at appropriate isotropic submanifolds of the groupoid in question, we find that the connecting map is expressed in terms of an explicit Wodzicki-type residue formula, which involves the jets of non-commutative symbols at the fixed-point set of the action.

scholarly journals Lefschetz-type fixed point theorems for spheric mappings

2018 ◽  
Vol 19 (2) ◽  
pp. 453-462
Author(s):  
Jan Andres ◽  
◽  
Lech Górniewicz ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Lefschetz Type

scholarly journals Holomorphic vector field and topological sigma model on ℂP1 worldsheet

2020 ◽  
Vol 35 (30) ◽  
pp. 2050192
Author(s):  
Masao Jinzenji ◽  
Ken Kuwata
Keyword(s):  
Fixed Point ◽  
Vector Field ◽  
Fixed Point Theorems ◽  
Sigma Model ◽  
Brst Symmetry ◽  
Killing Vector ◽  
Holomorphic Vector Field ◽  
Potential Term ◽  
Residue Formula ◽  
Holomorphic Vector Bundles

Witten suggested that fixed-point theorems can be derived by the supersymmetric sigma model on a Riemann manifold [Formula: see text] with potential terms induced from a Killing vector on [Formula: see text].3. One of the well-known fixed-point theorems is the Bott residue formula9 which represents the intersection number of Chern classes of holomorphic vector bundles on a Kähler manifold [Formula: see text] as the sum of contributions from fixed point sets of a holomorphic vector field [Formula: see text] on [Formula: see text]. In this paper, we derive the Bott residue formula by using the topological sigma model (A-model) that describes dynamics of maps from [Formula: see text] to [Formula: see text], with potential terms induced from the vector field [Formula: see text]. Our strategy is to restrict phase space of path integral to maps homotopic to constant maps. As an effect of adding a potential term to the topological sigma model, we are forced to modify the BRST symmetry of the original topological sigma model. Our potential term and BRST symmetry are closely related to the idea used in the paper by Beasley and Witten2 where potential terms induced from holomorphic section of a holomorphic vector bundle and corresponding supersymmetry are considered.

Mental equilibrium: Identifying fixed-point attractors in the stream of thought

2003 ◽  
Author(s):  
Robin R. Vallacher ◽  
Andrzej Nowak ◽  
Matthew Rockloff
Keyword(s):  
Fixed Point

ON THE RANDOM FIXED POINT THEOREMS IN ABSTRACT SPACE

1981 ◽  
Vol 1 (2) ◽  
pp. 133-144 ◽  
Author(s):  
Shaozhong Chen ◽  
Zuoshu Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Abstract Space ◽  
Random Fixed Point
Sign in / Sign up

Export Citation Format

Share Document