### Relative homological linking in critical point theory

#### Abstract

A relative homological linking of pairs is proposed. It is shown to

imply homotopical linking, as well as earlier non-relative notion of

homological linkings. Using Morse theory we prove a simple

"homological linking principle", thereby generalizing and

simplifying many well known results in critical point theory.

imply homotopical linking, as well as earlier non-relative notion of

homological linkings. Using Morse theory we prove a simple

"homological linking principle", thereby generalizing and

simplifying many well known results in critical point theory.

#### Keywords

Critical point theory; linking; Morse theory

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