Let <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="605_2025_2099_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="30" /> </InlineMediaObject> <EquationSource Format="TEX">$\Sigma _{g,p}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="normal">Σ</mi> <mrow> <mi>g</mi> <mo>,</mo> <mi>p</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> be an orientable surface of genus g and of finite type without boundary (i.e. an orientable closed surface with a finite number p of points removed). In this paper we study the <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="605_2025_2099_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">$\hbox {R}_{\infty }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>R</mtext> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation>-property for the surface pure braid groups <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="605_2025_2099_Article_IEq6.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="59" /> </InlineMediaObject> <EquationSource Format="TEX">$P_n(\Sigma _{g,p})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>P</mi> <mi>n</mi> </msub> <mrow> <mo stretchy="false">(</mo> <msub> <mi mathvariant="normal">Σ</mi> <mrow> <mi>g</mi> <mo>,</mo> <mi>p</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> as well as for the full surface braid groups <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="605_2025_2099_Article_IEq7.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="61" /> </InlineMediaObject> <EquationSource Format="TEX">$B_n(\Sigma _{g,p})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>B</mi> <mi>n</mi> </msub> <mrow> <mo stretchy="false">(</mo> <msub> <mi mathvariant="normal">Σ</mi> <mrow> <mi>g</mi> <mo>,</mo> <mi>p</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. We show that, with few exceptions, these groups have the <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="605_2025_2099_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">$\hbox {R}_{\infty }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>R</mtext> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation>-property.

The $\hbox {R}_{\infty }$-property for braid groups over orientable surfaces

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发表日期：

2025年7月7日

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Karel Dekimpe,
Daciberg Lima Gonçalves,
Oscar Ocampo

摘要

Let $\Sigma _{g,p}$ $Σ_{g, p}$ be an orientable surface of genus g and of finite type without boundary (i.e. an orientable closed surface with a finite number p of points removed). In this paper we study the $\hbox {R}_{\infty }$ $R_{\infty}$ -property for the surface pure braid groups $P_n(\Sigma _{g,p})$ $P_{n} (Σ_{g, p})$ as well as for the full surface braid groups $B_n(\Sigma _{g,p})$ $B_{n} (Σ_{g, p})$ . We show that, with few exceptions, these groups have the $\hbox {R}_{\infty }$ $R_{\infty}$ -property.

The \(\hbox {R}_{\infty }\)-property for braid groups over orientable surfaces

摘要