강연주제: Relative bounded cohomology
연사 : Park, HeeSook (박희숙) 박사
소속 : ASARC
날짜 : 11월 5일 수요일 (16:30~17:30)
장소 : ASARC 세미나실 (#1409)
초록 : We extend the homological algebra approach to the theory of the bounded cohomology from the absolute to the relative case. Moreover, we extend the theory of relative bounded cohomology from the usual case of a pair of spaces \( (X, Y) \) with \( Y \subset X \) to the
more general case of any continuous map \( Y \to X \) of spaces\( X \) and
\( Y \). Similarly, we extend a pair of groups \( (G, A) \) with \( A \subset G \) to any homomorphism \( A \to G \) of groups \( G \) and \( A \).
An important feature of the theory of the bounded cohomology is that the bounded cohomology of a connected topological space and its fundamental group coincide. Our general framework with continuous maps and homomorphisms turns out to be
necessary for comparing the relative bounded cohomology of spaces with the relative bounded cohomology of groups. With this, we prove that the relative bounded
cohomology of a continuous map \( Y \to X \) of spaces \( X \) and \( Y \) and
the relative bounded cohomology of the induced homomorphism \( \pi_{1}Y \to
\pi_{1}X \) coincide.
제목 : Relative bounded cohomology