The Lefschetz number and fiber preserving maps

Fixed Point Sets of Fiber-preserving Maps

Let F = (E, p, B;Y ) be a fiber bundle where E, B and Y are connected finite polyhedra. Let f : E → E be a fiber-preserving map and A ⊆ E a closed, locally contractible subset. We present necessary and sufficient conditions for A and its subsets to be the fixed point sets of maps fiber-homotopic to f . The necessary conditions correspond to those introduced by Schirmer in 1990 but, in the fiber...

Linear maps preserving or strongly preserving majorization on matrices

For $A,Bin M_{nm},$ we say that $A$ is left matrix majorized (resp. left matrix submajorized) by $B$ and write $Aprec_{ell}B$ (resp. $Aprec_{ell s}B$), if $A=RB$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $R.$ Moreover, we define the relation $sim_{ell s} $ on $M_{nm}$ as follows: $Asim_{ell s} B$ if $Aprec_{ell s} Bprec_{ell s} A.$ This paper characterizes all linear p...

On strongly Jordan zero-product preserving maps

In this paper, we give a characterization of strongly Jordan zero-product preserving maps on normed algebras as a generalization of  Jordan zero-product preserving maps. In this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly Jordan zero-product preserving maps are completely different. Also, we prove that the direct p...

A Survey of Invertibility and Spectrum Preserving Linear Maps

On Quantum Integrability and the Lefschetz Number

Certain phase space path integrals can be evaluated exactly using equivariant cohomology and localization in the canonical loop space. Here we extend this to a general class of models. We consider hamiltonians which are a priori arbitrary functions of the Cartan subalgebra generators of a Lie group which is defined on the phase space. We evaluate the corresponding path integral and find that it...