Forms and chain complexes II (Ex)

Definition 0.1 [Ranicki1980, Proposition 4.6] . An n-dimensional $\epsilon$$<wikitex>; {{beginthm|Definition|{{cite|Ranicki1980|Proposition 4.6}} }} An n-dimensional $\epsilon$-symmetric/$\epsilon$-quadratic) complex $(C, \phi)$/$(C, \psi)$ is called ''well-connected'' if $H_0(C)= 0$. {{endthm}} Show that the boundary of a well-connected \epsilon$-symmetric/$\epsilon$$\epsilon$-quadratic) complex $(C, \phi)$$(C, \phi)$/$(C, \psi)$$(C, \psi)$ is called well-connected if $H_0(C)= 0$$H_0(C)= 0$.

Show that the boundary of a well-connected $1$$1$-dimensional symmetric/quadratic complex gives a hyperbolic form.

See section 2 of [Ranicki1980]

References

• [Ranicki1980] A. Ranicki, The algebraic theory of surgery. I. Foundations, Proc. London Math. Soc. (3) 40 (1980), no.1, 87–192. MR560997 (82f:57024a) Zbl 0471.57012

$-dimensional symmetric/quadratic complex gives a hyperbolic form. See section 2 of {{cite|Ranicki1980}} == References == {{#RefList:}} [[Category:Exercises]] [[Category:Exercises without solution]]\epsilon-symmetric/$\epsilon$$\epsilon$-quadratic) complex $(C, \phi)$$(C, \phi)$/$(C, \psi)$$(C, \psi)$ is called well-connected if $H_0(C)= 0$$H_0(C)= 0$.