arXiv subjects

Philipp Wruck

Publications and source records attributed to Philipp Wruck.

3 recordsLinked to original sources

arXiv2013

Equivariant Lefschetz and Fuller indices via topological intersection theory

For a compact Lie group G, we use G-equivariant Poincaré duality for ordinary RO(G)-graded homology to define an equivariant intersection product, the dual of the equivariant cup product. Using this, we give a homological construction of the equivariant Lefschetz number and a simple proof of the equivariant Lefschetz fixed point theorem. With similar techniques, an equivariant Fuller index with values in the rationalized Burnside ring is constructed.

math.AT↗

arXiv2013

Genericity in equivariant dynamical systems and equivariant Fuller index theory

We define a notion of equivariant non-degeneracy of $G$-maps to introduce the class of equivariantly non-degenerate flows on smooth compact manifolds with compact Lie group action. We prove genericity of this class and use this result to construct an equivariant version of the Fuller index, which detects group orbits of periodic orbits of the flow, distinguished by their isotropy.

math.DS↗

arXiv2013

Axiomatic Description of Lefschetz Type Equivariant Homotopy Invariants

We describe generators of universal Lefschetz groups consisting of self-maps of equivariant 1-spheres. This allows to formulate a normalization axiom which, together with the usual axioms, determines an equivariant Lefschetz number uniquely. We apply this technique to identify the fixed orbit detecting equivariant Lefschetz number of Chorny with the fixed orbit index of Dzedzej.

math.AT↗