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• W1992553872 abstract "For any class <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper M> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>M</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {M}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of 4–manifolds, for instance the class <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper M left-parenthesis upper G right-parenthesis> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>M</mml:mi> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {M}(G)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of closed oriented manifolds with <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=pi 1 left-parenthesis upper M right-parenthesis approximately-equals upper G> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>π<!-- π --></mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo stretchy=false>(</mml:mo> <mml:mi>M</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>≅<!-- ≅ --></mml:mo> <mml:mi>G</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>pi _1(M) cong G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for a fixed group <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=application/x-tex>G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, the geography of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper M> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>M</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {M}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the set of integer pairs <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=StartSet left-parenthesis sigma left-parenthesis upper M right-parenthesis comma chi left-parenthesis upper M right-parenthesis right-parenthesis vertical-bar upper M element-of script upper M EndSet> <mml:semantics> <mml:mrow> <mml:mo fence=false stretchy=false>{</mml:mo> <mml:mo stretchy=false>(</mml:mo> <mml:mi>σ<!-- σ --></mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>M</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>,</mml:mo> <mml:mi>χ<!-- χ --></mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>M</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo stretchy=false>)</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo stretchy=false>|</mml:mo> </mml:mrow> <mml:mi>M</mml:mi> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>M</mml:mi> </mml:mrow> <mml:mo fence=false stretchy=false>}</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>{(sigma (M), chi (M)) | M in mathcal {M}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=sigma> <mml:semantics> <mml:mi>σ<!-- σ --></mml:mi> <mml:annotation encoding=application/x-tex>sigma</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=chi> <mml:semantics> <mml:mi>χ<!-- χ --></mml:mi> <mml:annotation encoding=application/x-tex>chi</mml:annotation> </mml:semantics> </mml:math> </inline-formula> denote the signature and Euler characteristic. This paper explores general properties of the geography of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper M left-parenthesis upper G right-parenthesis> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>M</mml:mi> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {M}(G)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and undertakes an extended study of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper M left-parenthesis bold upper Z Superscript n Baseline right-parenthesis> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>M</mml:mi> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=bold>Z</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>mathcal {M}(mathbf {Z}^n)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>." @default.
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• W1992553872 date "2009-03-16" @default.
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• W1992553872 title "The geography problem for 4-manifolds with specified fundamental group" @default.
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