Formations and chain complexes II (Ex)
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| + | {{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}} | ||
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| + | {{beginthm|Exercise}} | ||
Show that a boundary of a well-connected $2$-dimensional symmetric/quadratic complex gives a boundary formation. | Show that a boundary of a well-connected $2$-dimensional symmetric/quadratic complex gives a boundary formation. | ||
| + | {{endthm}} | ||
See section 2 of {{cite|Ranicki1980}} | See section 2 of {{cite|Ranicki1980}} | ||
Revision as of 16:20, 31 May 2012
Definition 0.1 [Ranicki1980, Proposition 4.6] .
An n-dimensional 
-symmetric(-quadratic) complex 
(
) is called well-connected if 
.
Exercise 0.2.
Show that a boundary of a well-connected 
-dimensional symmetric/quadratic complex gives a boundary formation.
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
