03512nam0 22004933i 450 VAN0026783520260629122818.75N978146849367279917928520231124d1975 |0itac50 baengUS|||| |||||i e bcrApplications of Algebraic TopologyGraphs and Networks, The Picard-Lefschetz Theory and Feynman IntegralsS. LefschetzNew YorkSpringer-Verlag1975viii, 191 p.ill.24 cmThis monograph is based, in part, upon lectures given in the Princeton School of Engineering and Applied Science. It presupposes mainly an elementary knowledge of linear algebra and of topology. In topology the limit is dimension two mainly in the latter chapters and questions of topological invariance are carefully avoided. From the technical viewpoint graphs is our only requirement. However, later, questions notably related to Kuratowski's classical theorem have demanded an easily provided treatment of 2-complexes and surfaces. January 1972 Solomon Lefschetz 4 INTRODUCTION The study of electrical networks rests upon preliminary theory of graphs. In the literature this theory has always been dealt with by special ad hoc methods. My purpose here is to show that actually this theory is nothing else than the first chapter of classical algebraic topology and may be very advantageously treated as such by the well known methods of that science. Part I of this volume covers the following ground: The first two chapters present, mainly in outline, the needed basic elements of linear algebra. In this part duality is dealt with somewhat more extensively. In Chapter III the merest elements of general topology are discussed. Graph theory proper is covered in Chapters IV and v, first structurally and then as algebra. Chapter VI discusses the applications to networks. In Chapters VII and VIII the elements of the theory of 2-dimensional complexes and surfaces are presented.001VAN000237172001 Applied mathematical sciences210 Berlin [etc]Springer1971-1655-XXAlgebraic topology [MSC 2020]VANC019672MF57-XXManifolds and cell complexes [MSC 2020]VANC019671MF57M15Relations of low-dimensional topology with graph theory [MSC 2020]VANC023654MF57Q05General topology of complexes [MSC 2020]VANC031231MFAlgebraicKW:KAlgebraic TopologyKW:KApplicationsKW:KGraphsKW:KHomotopyKW:KTopologyKW:KVector spacesKW:KUSNew YorkVANL000011LefschetzSolomonVANV04237512523Springer <editore>VANV108073650Lefschetz, S.Lefschetz, SolomonVANV262533ITSOL20260911RICAhttps://doi.org/10.1007/978-1-4684-9367-2E-book – Accesso al full-text attraverso riconoscimento IP di Ateneo, proxy e/o ShibbolethBIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICAIT-CE0120VAN08NVAN00267835BIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA08DLOAD e-book 7328 08eMF7328 20231127 Applications of algebraic topology382114UNICAMPANIA