Normal bordism - definitions (Ex)

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<wikitex>;
In these exercises we use the notation of {{citeD|Lück2001|Section 3}}
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In these exercises we use the notation of {{citeD|Lück2001|Section 3.3}}
{{beginthm|Exercise}} \label{ex:nb}
{{beginthm|Exercise}} \label{ex:nb}
Modify the definition of $\Omega_n(\xi)$ in order to obtain the definition of $\mathcal{N}_n(X,k)$.
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Modify the definition of $\Omega_n(\xi)$ in order to obtain the definition of the normal maps $\mathcal{N}_n(X,k)$.
{{endthm}}
{{endthm}}
{{beginrem|Hint}}
{{beginrem|Hint}}
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{{endrem}}
{{endrem}}
{{beginthm|Exercise}}
{{beginthm|Exercise}}
Repeat exercise \ref{ex:nb} for the tangential normal invariants $\mathcal{N}_n^T(X)$.
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Repeat exercise \ref{ex:nb} for the tangential normal maps $\mathcal{N}_n^T(X)$.
{{endthm}}
{{endthm}}
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</wikitex>

Revision as of 11:45, 2 April 2012

In these exercises we use the notation of [Lück2001, Section 3.3]

Exercise 0.1. Modify the definition of \Omega_n(\xi) in order to obtain the definition of the normal maps \mathcal{N}_n(X,k).

Hint 0.2. Note: There should a be a map F:W\to X\times[0,1] of degree one involved.

Exercise 0.3. Repeat exercise 0.1 for the tangential normal maps \mathcal{N}_n^T(X).

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