Beschreibung:
<p>The influence of the Poincaré Conjecture on the following problem of M. Cohen is examined. <italic>Problem</italic>. Does there exist a four-dimensional <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="h">
<mml:semantics>
<mml:mi>h</mml:mi>
<mml:annotation encoding="application/x-tex">h</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula>-cobordism with nontrivial Whitehead torsion? It is proved (assuming the Poincarè Conjecture) that none of the following groups may be the fundamental group of a <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="4">
<mml:semantics>
<mml:mn>4</mml:mn>
<mml:annotation encoding="application/x-tex">4</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula>-dimensional <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="h">
<mml:semantics>
<mml:mi>h</mml:mi>
<mml:annotation encoding="application/x-tex">h</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula>-corbordism with nontrivial Whitehead torsion: generalized quaternion groups, cyclic groups <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper Z 8">
<mml:semantics>
<mml:mrow class="MJX-TeXAtom-ORD">
<mml:msub>
<mml:mi>Z</mml:mi>
<mml:mn>8</mml:mn>
</mml:msub>
</mml:mrow>
<mml:annotation encoding="application/x-tex">{Z_8}</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula>, <inline-formula content-type="math/mathml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper Z 12">
<mml:semantics>
<mml:mrow class="MJX-TeXAtom-ORD">
<mml:msub>
<mml:mi>Z</mml:mi>
<mml:mrow class="MJX-TeXAtom-ORD">
<mml:mn>12</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:annotation encoding="application/x-tex">{Z_{12}}</mml:annotation>
</mml:semantics>
</mml:math>
</inline-formula>, the binary octahedral group, the binary tetrahedral group.</p>