Question about "THE MORSE INEQUALITIES"in Milnor's book

Question

in this paragraph what is $H_{*}$ ?

Please help me

Thank you .

Answer 1

$H_*$ is homology. An equation $H_*(\text {this})=H_*(\text{that})$ means that $H_k(\text {this})=H_k(\text{that})$ for all $k$.

Answer 2

Singular homology. There is a homology group $H_q$ in each dimension $q \ge 0$, and $H_*$ refers to all of them at once.