Cross-caps, triple points and a linking invariant for finitely determined germs
It was recently proved that for finitely determined germs $ \Phi: ( \mathbb{C}^2, 0) \to ( \mathbb{C}^3, 0) $ the number $C(\Phi)$ of Whitney umbrella points and the number $T(\Phi)$ of triple values of a stable deformation are topological invariants. The proof uses the fact that the combination $C(...
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| creator | Pintér, Gergő Sándor, András |
| description | It was recently proved that for finitely determined germs $ \Phi: (
\mathbb{C}^2, 0) \to ( \mathbb{C}^3, 0) $ the number $C(\Phi)$ of Whitney
umbrella points and the number $T(\Phi)$ of triple values of a stable
deformation are topological invariants. The proof uses the fact that the
combination $C(\Phi)-3T(\Phi)$ is topological since it equals the linking
invariant of the associated immersion $S^3 \looparrowright S^5$ introduced by
Ekholm and Sz\H{u}cs. We provide a new, direct proof for this equality. We also
clarify the relation between various definitions of the latter invariant. |
| doi_str_mv | 10.48550/arxiv.2202.05828 |
| format | Article |
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\mathbb{C}^2, 0) \to ( \mathbb{C}^3, 0) $ the number $C(\Phi)$ of Whitney
umbrella points and the number $T(\Phi)$ of triple values of a stable
deformation are topological invariants. The proof uses the fact that the
combination $C(\Phi)-3T(\Phi)$ is topological since it equals the linking
invariant of the associated immersion $S^3 \looparrowright S^5$ introduced by
Ekholm and Sz\H{u}cs. We provide a new, direct proof for this equality. We also
clarify the relation between various definitions of the latter invariant.</description><identifier>DOI: 10.48550/arxiv.2202.05828</identifier><language>eng</language><subject>Mathematics - Algebraic Geometry ; Mathematics - Algebraic Topology ; Mathematics - Complex Variables</subject><creationdate>2022-02</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2202.05828$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2202.05828$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Pintér, Gergő</creatorcontrib><creatorcontrib>Sándor, András</creatorcontrib><title>Cross-caps, triple points and a linking invariant for finitely determined germs</title><description>It was recently proved that for finitely determined germs $ \Phi: (
\mathbb{C}^2, 0) \to ( \mathbb{C}^3, 0) $ the number $C(\Phi)$ of Whitney
umbrella points and the number $T(\Phi)$ of triple values of a stable
deformation are topological invariants. The proof uses the fact that the
combination $C(\Phi)-3T(\Phi)$ is topological since it equals the linking
invariant of the associated immersion $S^3 \looparrowright S^5$ introduced by
Ekholm and Sz\H{u}cs. We provide a new, direct proof for this equality. We also
clarify the relation between various definitions of the latter invariant.</description><subject>Mathematics - Algebraic Geometry</subject><subject>Mathematics - Algebraic Topology</subject><subject>Mathematics - Complex Variables</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotz71OwzAUhmEvDKhwAUz4AkjwTxw7I4r4kyp16R6d2MfVEakT2VFF755SmN5v-qSHsQcp6sYZI54hf9OpVkqoWhin3C3b9XkupfKwlCe-Zlom5MtMaS0cUuDAJ0pflA6c0gkyQVp5nDOPlGjF6cwDrpiPlDDww2WUO3YTYSp4_98N27-97vuPart7_-xfthW01lVBRye17ayRqLz23WiDRXAoOyfaUSrTNB7bJprRKxsVxAheKIVjvMRKvWGPf7dX0bBkOkI-D7-y4SrTPyWpSeE</recordid><startdate>20220211</startdate><enddate>20220211</enddate><creator>Pintér, Gergő</creator><creator>Sándor, András</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20220211</creationdate><title>Cross-caps, triple points and a linking invariant for finitely determined germs</title><author>Pintér, Gergő ; Sándor, András</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a678-d3f81379751e2c3c9b7d7ea8e19806b12544ce64f5bc27f2affac022ebfc02713</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Mathematics - Algebraic Geometry</topic><topic>Mathematics - Algebraic Topology</topic><topic>Mathematics - Complex Variables</topic><toplevel>online_resources</toplevel><creatorcontrib>Pintér, Gergő</creatorcontrib><creatorcontrib>Sándor, András</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Pintér, Gergő</au><au>Sándor, András</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Cross-caps, triple points and a linking invariant for finitely determined germs</atitle><date>2022-02-11</date><risdate>2022</risdate><abstract>It was recently proved that for finitely determined germs $ \Phi: (
\mathbb{C}^2, 0) \to ( \mathbb{C}^3, 0) $ the number $C(\Phi)$ of Whitney
umbrella points and the number $T(\Phi)$ of triple values of a stable
deformation are topological invariants. The proof uses the fact that the
combination $C(\Phi)-3T(\Phi)$ is topological since it equals the linking
invariant of the associated immersion $S^3 \looparrowright S^5$ introduced by
Ekholm and Sz\H{u}cs. We provide a new, direct proof for this equality. We also
clarify the relation between various definitions of the latter invariant.</abstract><doi>10.48550/arxiv.2202.05828</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Algebraic Geometry Mathematics - Algebraic Topology Mathematics - Complex Variables |
| title | Cross-caps, triple points and a linking invariant for finitely determined germs |
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