rp2 $\mathbb {R}P^2$和rp2∧cp2 $\mathbb {R}P^2 \wedge \mathbb {C}P^2$的拓扑模形式

Pub Date : 2022-09-19 DOI:10.1112/topo.12263

Agnès Beaudry, Irina Bobkova, Viet-Cuong Pham, Zhouli Xu

{"title":"rp2 $\\mathbb {R}P^2$和rp2∧cp2 $\\mathbb {R}P^2 \\wedge \\mathbb {C}P^2$的拓扑模形式","authors":"Agnès Beaudry, Irina Bobkova, Viet-Cuong Pham, Zhouli Xu","doi":"10.1112/topo.12263","DOIUrl":null,"url":null,"abstract":"<p>We study the elliptic spectral sequence computing <math>\n <semantics>\n <mrow>\n <mi>t</mi>\n <mi>m</mi>\n <msub>\n <mi>f</mi>\n <mo>∗</mo>\n </msub>\n <mrow>\n <mo>(</mo>\n <mi>R</mi>\n <msup>\n <mi>P</mi>\n <mn>2</mn>\n </msup>\n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation>$tmf_*(\\mathbb {R}P^2)$</annotation>\n </semantics></math> and <math>\n <semantics>\n <mrow>\n <mi>t</mi>\n <mi>m</mi>\n <msub>\n <mi>f</mi>\n <mo>∗</mo>\n </msub>\n <mrow>\n <mo>(</mo>\n <mi>R</mi>\n <msup>\n <mi>P</mi>\n <mn>2</mn>\n </msup>\n <mo>∧</mo>\n <mi>C</mi>\n <msup>\n <mi>P</mi>\n <mn>2</mn>\n </msup>\n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation>$tmf_* (\\mathbb {R} P^2 \\wedge \\mathbb {C} P^2)$</annotation>\n </semantics></math>. Specifically, we compute all differentials and resolve exotic extensions by 2, <math>\n <semantics>\n <mi>η</mi>\n <annotation>$\\eta$</annotation>\n </semantics></math>, and <math>\n <semantics>\n <mi>ν</mi>\n <annotation>$\\nu$</annotation>\n </semantics></math>. For <math>\n <semantics>\n <mrow>\n <mi>t</mi>\n <mi>m</mi>\n <msub>\n <mi>f</mi>\n <mo>∗</mo>\n </msub>\n <mrow>\n <mo>(</mo>\n <mi>R</mi>\n <msup>\n <mi>P</mi>\n <mn>2</mn>\n </msup>\n <mo>∧</mo>\n <mi>C</mi>\n <msup>\n <mi>P</mi>\n <mn>2</mn>\n </msup>\n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation>$tmf_* (\\mathbb {R} P^2 \\wedge \\mathbb {C} P^2)$</annotation>\n </semantics></math>, we also compute the effect of the <math>\n <semantics>\n <msub>\n <mi>v</mi>\n <mn>1</mn>\n </msub>\n <annotation>$v_1$</annotation>\n </semantics></math>-self maps of <math>\n <semantics>\n <mrow>\n <mi>R</mi>\n <msup>\n <mi>P</mi>\n <mn>2</mn>\n </msup>\n <mo>∧</mo>\n <mi>C</mi>\n <msup>\n <mi>P</mi>\n <mn>2</mn>\n </msup>\n </mrow>\n <annotation>$\\mathbb {R} P^2 \\wedge \\mathbb {C} P^2$</annotation>\n </semantics></math> on <math>\n <semantics>\n <mrow>\n <mi>t</mi>\n <mi>m</mi>\n <mi>f</mi>\n </mrow>\n <annotation>$tmf$</annotation>\n </semantics></math>-homology.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"The topological modular forms of \\n \\n \\n R\\n \\n P\\n 2\\n \\n \\n $\\\\mathbb {R}P^2$\\n and \\n \\n \\n R\\n \\n P\\n 2\\n \\n ∧\\n C\\n \\n P\\n 2\\n \\n \\n $\\\\mathbb {R}P^2 \\\\wedge \\\\mathbb {C}P^2$\",\"authors\":\"Agnès Beaudry, Irina Bobkova, Viet-Cuong Pham, Zhouli Xu\",\"doi\":\"10.1112/topo.12263\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We study the elliptic spectral sequence computing <math>\\n <semantics>\\n <mrow>\\n <mi>t</mi>\\n <mi>m</mi>\\n <msub>\\n <mi>f</mi>\\n <mo>∗</mo>\\n </msub>\\n <mrow>\\n <mo>(</mo>\\n <mi>R</mi>\\n <msup>\\n <mi>P</mi>\\n <mn>2</mn>\\n </msup>\\n <mo>)</mo>\\n </mrow>\\n </mrow>\\n <annotation>$tmf_*(\\\\mathbb {R}P^2)$</annotation>\\n </semantics></math> and <math>\\n <semantics>\\n <mrow>\\n <mi>t</mi>\\n <mi>m</mi>\\n <msub>\\n <mi>f</mi>\\n <mo>∗</mo>\\n </msub>\\n <mrow>\\n <mo>(</mo>\\n <mi>R</mi>\\n <msup>\\n <mi>P</mi>\\n <mn>2</mn>\\n </msup>\\n <mo>∧</mo>\\n <mi>C</mi>\\n <msup>\\n <mi>P</mi>\\n <mn>2</mn>\\n </msup>\\n <mo>)</mo>\\n </mrow>\\n </mrow>\\n <annotation>$tmf_* (\\\\mathbb {R} P^2 \\\\wedge \\\\mathbb {C} P^2)$</annotation>\\n </semantics></math>. Specifically, we compute all differentials and resolve exotic extensions by 2, <math>\\n <semantics>\\n <mi>η</mi>\\n <annotation>$\\\\eta$</annotation>\\n </semantics></math>, and <math>\\n <semantics>\\n <mi>ν</mi>\\n <annotation>$\\\\nu$</annotation>\\n </semantics></math>. For <math>\\n <semantics>\\n <mrow>\\n <mi>t</mi>\\n <mi>m</mi>\\n <msub>\\n <mi>f</mi>\\n <mo>∗</mo>\\n </msub>\\n <mrow>\\n <mo>(</mo>\\n <mi>R</mi>\\n <msup>\\n <mi>P</mi>\\n <mn>2</mn>\\n </msup>\\n <mo>∧</mo>\\n <mi>C</mi>\\n <msup>\\n <mi>P</mi>\\n <mn>2</mn>\\n </msup>\\n <mo>)</mo>\\n </mrow>\\n </mrow>\\n <annotation>$tmf_* (\\\\mathbb {R} P^2 \\\\wedge \\\\mathbb {C} P^2)$</annotation>\\n </semantics></math>, we also compute the effect of the <math>\\n <semantics>\\n <msub>\\n <mi>v</mi>\\n <mn>1</mn>\\n </msub>\\n <annotation>$v_1$</annotation>\\n </semantics></math>-self maps of <math>\\n <semantics>\\n <mrow>\\n <mi>R</mi>\\n <msup>\\n <mi>P</mi>\\n <mn>2</mn>\\n </msup>\\n <mo>∧</mo>\\n <mi>C</mi>\\n <msup>\\n <mi>P</mi>\\n <mn>2</mn>\\n </msup>\\n </mrow>\\n <annotation>$\\\\mathbb {R} P^2 \\\\wedge \\\\mathbb {C} P^2$</annotation>\\n </semantics></math> on <math>\\n <semantics>\\n <mrow>\\n <mi>t</mi>\\n <mi>m</mi>\\n <mi>f</mi>\\n </mrow>\\n <annotation>$tmf$</annotation>\\n </semantics></math>-homology.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2022-09-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/topo.12263\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/topo.12263","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 1

摘要

研究了椭圆谱序列计算tmf∗(R p2)$ tmf_*(\mathbb {R}P^2)$和tmf * (rp2∧cp2) $tmf_* (\mathbb {R} P^2 \wedge\mathbb {C} P^2)$。具体来说，我们计算了所有的微分，并通过2，η $\eta$和ν $\nu$来解析奇异的扩展。对于t m f * (rp2∧cp2)$tmf_* (\mathbb {R} P^2 \wedge \mathbb {C} P^2)$，我们还计算了rp2∧cp2 $\mathbb {R} P^2 \wedge \mathbb {C} P^2$的v1 $v_1$ -自映射的作用T mf$ tmf$ -同源性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

The topological modular forms of R P 2 $\mathbb {R}P^2$ and R P 2 ∧ C P 2 $\mathbb {R}P^2 \wedge \mathbb {C}P^2$

We study the elliptic spectral sequence computing $t m f_{*} (R P^{2})$ and $t m f_{*} (R P^{2} \land C P^{2})$ . Specifically, we compute all differentials and resolve exotic extensions by 2, $η$ , and $ν$ . For $t m f_{*} (R P^{2} \land C P^{2})$ , we also compute the effect of the $v_{1}$ -self maps of $R P^{2} \land C P^{2}$ on $t m f$ -homology.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助