Lefschetz Theory on Manifolds with Singularities

2006 ◽  
pp. 157-186 ◽  
Author(s):  
Vladimir Nazaikinskii ◽  
Boris Sternin
Keyword(s):  
Manifolds With Singularities

scholarly journals Surgery and the relative index in elliptic theory

2006 ◽  
Vol 2006 ◽  
pp. 1-16 ◽  
Author(s):  
V. E. Nazaikinskii ◽  
B. Yu. Sternin
Keyword(s):  
Integral Operators ◽  
Fourier Integral ◽  
Fourier Integral Operators ◽  
Relative Index ◽  
Survey Article ◽  
General Index ◽  
Elliptic Theory ◽  
Locality Principle ◽  
Index Formulas ◽  
Manifolds With Singularities

This is a survey article featuring the general index locality principle introduced by the authors, which can be used to obtain index formulas for elliptic operators and Fourier integral operators in various situations, including operators on stratified manifolds and manifolds with singularities.

Realization of homology classes of PL-manifolds with singularities

1987 ◽  
Vol 41 (5) ◽  
pp. 417-422
Author(s):  
Yu. B. Rudyak
Keyword(s):  
Manifolds With Singularities

scholarly journals Structural stability of attractor–repellor endomorphisms with singularities

2011 ◽  
Vol 32 (1) ◽  
pp. 1-33
Author(s):  
PIERRE BERGER
Keyword(s):  
Structural Stability ◽  
Compact Subset ◽  
Disjoint Union ◽  
Singularity Theory ◽  
Compact Manifolds ◽  
Hyperbolic Attractor ◽  
Manifolds With Singularities

AbstractWe prove a theorem on the structural stability of smooth attractor–repellor endomorphisms of compact manifolds, with singularities. By attractor–repellor, we mean that the non-wandering set of the dynamics f is the disjoint union of an expanding compact subset with a hyperbolic attractor on which f acts bijectively. The statement of this result is both infinitesimal and dynamical. To our knowledge, this is the first in this hybrid direction. Our results also generalize Mather’s theorem in singularity theory, which states that infinitesimal stability implies structural stability for composed mappings to the larger category of laminations.

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