Diffeomorphisms of manifolds with finite fundamental group

Abstract

We show that the group <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper D left-parenthesis upper M right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">D</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>M</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathcal {D}(M)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of pseudoisotopy classes of diffeomorphisms of a manifold of dimension <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="greater-than-or-equal-to 5"> <mml:semantics> <mml:mrow> <mml:mo>≥<!-- ≥ --></mml:mo> <mml:mn>5</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">\geq 5</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and of finite fundamental group is commensurable to an arithmetic group. As a result <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="pi 0 left-parenthesis upper D i f f upper M right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>π<!-- π --></mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>D</mml:mi> <mml:mi>i</mml:mi> <mml:mi>f</mml:mi> <mml:mi>f</mml:mi> <mml:mspace width="thinmathspace" /> <mml:mi>M</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">{\pi _0}(Diff\,M)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a group of finite type.

Locations

• arXiv (Cornell University) - View - PDF
• Bulletin of the American Mathematical Society - View - PDF