Browder-Livesay index invariant and equivariant knots.

An equivariant Casson invariant of knots in homology spheres

From the construction of the Casson invariant of homology spheres using intersection on configuration spaces, we propose a construction of an equivariant Casson invariant for a knot K homologous to 0 in rational homology sphere M . Our construction is adapted from C. Lescop ([7]) and use the same ideas in an equivariant setting. We show that the invariant we obtain is similar to the 2-loop part...

On Equivariant Slice Knots

We suggest a method to detect that two periodic knots are not equivariantly concordant, using surgery on factor links. We construct examples which satisfy all known necessary conditions for equivariant slice knots — Naik’s and Choi-Ko-Song’s improvements of classical results on Seifert forms and Casson-Gordon invariants of slice knots — but are not equivariantly slice. Introduction An oriented ...

Modeling of ‎I‎nfinite Divisible Distributions Using Invariant and Equivariant Functions

‎Basu’s theorem is one of the most elegant results of classical statistics‎. ‎Succinctly put‎, ‎the theorem says‎: ‎if T is a complete sufficient statistic for a family of probability measures‎, ‎and V is an ancillary statistic‎, ‎then T and V are independent‎. ‎A very novel application of Basu’s theorem appears recently in proving the infinite divisibility of certain statistics‎. ‎In addition ...

On Equivariant Slice Knots

We suggest a method to detect that two periodic knots are not equivariantly concordant, using surgery on factor links. We construct examples which satisfy all known necessary conditions for equivariant slice knots— Naik’s and Choi-Ko-Song’s improvements of classical results on Seifert forms and Casson-Gordon invariants of slice knots — but are not equivariantly slice.

The equivariant Chern character and index of G-invariant Operators