{"title":"Spectral Gap for the Cohomological Laplacian of SL3(ℤ)","authors":"Marek Kaluba, Piotr Mizerka, Piotr W. Nowak","doi":"10.1080/10586458.2024.2333722","DOIUrl":null,"url":null,"abstract":"We show that the cohomological Laplacian in degree 1 in the group cohomology of SL3(Z) is a sum of hermitian squares in the algebra Mn(RG). We provide an estimate of the spectral gap for this Lapla...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":"17 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Experimental Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/10586458.2024.2333722","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
We show that the cohomological Laplacian in degree 1 in the group cohomology of SL3(Z) is a sum of hermitian squares in the algebra Mn(RG). We provide an estimate of the spectral gap for this Lapla...
期刊介绍：
Experimental Mathematics publishes original papers featuring formal results inspired by experimentation, conjectures suggested by experiments, and data supporting significant hypotheses.
Experiment has always been, and increasingly is, an important method of mathematical discovery. (Gauss declared that his way of arriving at mathematical truths was "through systematic experimentation.") Yet this tends to be concealed by the tradition of presenting only elegant, fully developed, and rigorous results.
Experimental Mathematics was founded in the belief that theory and experiment feed on each other, and that the mathematical community stands to benefit from a more complete exposure to the experimental process. The early sharing of insights increases the possibility that they will lead to theorems: An interesting conjecture is often formulated by a researcher who lacks the techniques to formalize a proof, while those who have the techniques at their fingertips have been looking elsewhere. Even when the person who had the initial insight goes on to find a proof, a discussion of the heuristic process can be of help, or at least of interest, to other researchers. There is value not only in the discovery itself, but also in the road that leads to it.
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