A bstract . Let E ð 1 Þ be the first Johnson-Wilson spectrum at the prime two. In this paper, we calculate the homotopy groups of the E ð 1 Þ -localized sphere spectrum with a grading over the Picard group of the stable homotopy category of E ð 1 Þ -local spectra.
{"title":"The $E(1)$-local Picard graded homotopy groups of the sphere spectrum at the prime two","authors":"Ryo Kato","doi":"10.32917/hmj/1595901623","DOIUrl":"https://doi.org/10.32917/hmj/1595901623","url":null,"abstract":"A bstract . Let E ð 1 Þ be the first Johnson-Wilson spectrum at the prime two. In this paper, we calculate the homotopy groups of the E ð 1 Þ -localized sphere spectrum with a grading over the Picard group of the stable homotopy category of E ð 1 Þ -local spectra.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46174954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A bstract . For a given angle y , consider the configuration space C n of equilateral n -gons in R 3 whose bond angles are equal to y except for two successive ones. We show that when n b 8 and y is su‰ciently close to the inner angle n (cid:1) 2 n p of the regular n -gon, C n is homeomorphic to the ð n (cid:1) 4 Þ -dimensional sphere S n (cid:1) 4 .
一个混蛋。For a赐予安格尔y,认为《configuration太空equilateral之C n n -gons在R 3是谁的邦德angles equal to y除了For two successive势力。我们表演那8当n b和y是苏‰ciently接近《内在安格尔n (cid): 1)普通之2 n p n -gon C, n是homeomorphicðn (cid》:1)4Þ-dimensional范围S n (cid: 1) 4。
{"title":"The configuration space of almost regular polygons","authors":"S. Goto, Kazushi Komatsu, Junya Yagi","doi":"10.32917/hmj/1595901626","DOIUrl":"https://doi.org/10.32917/hmj/1595901626","url":null,"abstract":"A bstract . For a given angle y , consider the configuration space C n of equilateral n -gons in R 3 whose bond angles are equal to y except for two successive ones. We show that when n b 8 and y is su‰ciently close to the inner angle n (cid:1) 2 n p of the regular n -gon, C n is homeomorphic to the ð n (cid:1) 4 Þ -dimensional sphere S n (cid:1) 4 .","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45875146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A bstract . Let N g be the non-orientable surface of genus g , MCG ð N g Þ the mapping class group of N g , T ð N g Þ the index 2 subgroup generated by all Dehn twists of MCG ð N g Þ . We prove that for odd genus, (1) if g ¼ 4 k þ 3 ð k b 1 Þ , MCG ð N g Þ can be generated by three elements of finite order; (2) if g ¼ 4 k þ 1 ð k b 2 Þ , T ð N g Þ can be generated by three elements of finite order.
一个混蛋。让N g属non-orientable地表》成为g, MCGðN g绘图课集团》Þg, TðN gÞ《指数2 subgroup generated by所有Dehn扭曲了的MCGðN gÞ。我们证明那个奇怪的,(1)如果g¼属4 kþ3ðk b 1Þ,MCGðN gÞ可以成为generated byfinite秩序的三个文本;(2)如果g¼4 kþ1,2Þ,Tððk b N gÞ可以成为generated by三个finite命令的文本。
{"title":"The torsion generating set of the mapping class groups and the Dehn twist subgroups of non-orientable surfaces of odd genus","authors":"Xiaoming Du","doi":"10.32917/hmj/1595901627","DOIUrl":"https://doi.org/10.32917/hmj/1595901627","url":null,"abstract":"A bstract . Let N g be the non-orientable surface of genus g , MCG ð N g Þ the mapping class group of N g , T ð N g Þ the index 2 subgroup generated by all Dehn twists of MCG ð N g Þ . We prove that for odd genus, (1) if g ¼ 4 k þ 3 ð k b 1 Þ , MCG ð N g Þ can be generated by three elements of finite order; (2) if g ¼ 4 k þ 1 ð k b 2 Þ , T ð N g Þ can be generated by three elements of finite order.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47104146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
It is well-known that the second coefficient of the Alexander polynomial of any lens space knot in $S^3$ is $-1$. We show that the non-zero third coefficient condition of the Alexander polynomial of a lens space knot $K$ in $S^3$ confines the surgery to the one realized by the $(2,2g+1)$-torus knot, where $g$ is the genus of $K$. In particular, such a lens surgery polynomial coincides with $Delta_{T(2,2g+1)}(t)$.
{"title":"The third term in lens surgery\u0000 polynomials","authors":"M. Tange","doi":"10.32917/H2020050","DOIUrl":"https://doi.org/10.32917/H2020050","url":null,"abstract":"It is well-known that the second coefficient of the Alexander polynomial of any lens space knot in $S^3$ is $-1$. We show that the non-zero third coefficient condition of the Alexander polynomial of a lens space knot $K$ in $S^3$ confines the surgery to the one realized by the $(2,2g+1)$-torus knot, where $g$ is the genus of $K$. In particular, such a lens surgery polynomial coincides with $Delta_{T(2,2g+1)}(t)$.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2020-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44488644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}