Article

Lefschetz Theory on Manifolds with Singularities

05/2002;
Source: CiteSeer

ABSTRACT The semiclassical method in Lefschetz theory is presented and applied to the computation of Lefschetz numbers of endomorphisms of elliptic complexes on manifolds with singularities. Two distinct cases are considered, one in which the endomorphism is geometric and the other in which the endomorphism is speci ed by Fourier integral operators associated with a canonical transformation. In the latter case, the problem includes a small parameter and the formulas are (semiclassically) asymptotic. In the rst case, the parameter is introduced arti cially and the semiclassical method gives exact answers. In both cases, the Lefschetz number is the sum of contributions of interior xed points given (in the case of geometric endomorphisms) by standard formulas plus the contribution of xed singular points.

0 0
 · 
0 Bookmarks
 · 
22 Views
Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.

Full-text (2 Sources)

View
3 Downloads
Available from
15 Apr 2013

Keywords

arti cially
 
canonical transformation
 
cases
 
computation
 
contributions
 
distinct cases
 
endomorphism
 
endomorphisms
 
exact answers
 
Fourier integral operators
 
geometric endomorphisms
 
interior xed points
 
manifolds
 
rst case
 
semiclassical method
 
semiclassically
 
small parameter
 
standard formulas
 
xed singular points