The signature and arithmetic genus of certain aspherical manifolds

F. T. Farrell

Type: Article

Publication Date: 1976-01-01

Citations: 1

DOI: https://doi.org/10.1090/s0002-9939-1976-0407855-1

Abstract

In this paper we show that the signature and arithmetic genus of certain aspherical manifolds <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M"> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding="application/x-tex">M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> vanish when the center of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="pi 1 upper M"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>π</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">{\pi _1}M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is nontrivial. We make the possibly technical assumption that <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="pi 1 upper M"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>π</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">{\pi _1}M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is residually finite.

Locations

Proceedings of the American Mathematical Society - View - PDF

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+	The Index of Elliptic Operators: III	1968	Michael Atiyah I. M. Singer
+	Compact Clifford-Klein forms of symmetric spaces	1963	Armand Borel
+	A Lefschetz Fixed Point Formula for Elliptic Complexes: II. Applications	1968	Michael Atiyah R. Bott
+	Centerless groups—an algebraic formulation of Gottlieb’s theorem	1965	John R. Stallings
+	Topological Methods in Algebraic Geometry	1966	Friedrich Hirzebruch