Applications and Computations
摘要
In this chapter we demonstrate the effectiveness of twisted Morse complexes by collecting and expanding on some applications of homology and cohomology with local coefficients. We discuss relationships between parallel 1-forms and Lichnerowicz cohomology, and we show how to use twisted Morse cohomology to explicitly compute the Lichnerowicz cohomology of a surface. We also discuss Morse theoretic obstructions to a space being an associative H-space. Furthermore, we discuss Novikov homologyNovikov homology and show how Novikov numbers can be computed using the results in Chaps. 4 and 5 .