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Absolute Homology, Representations and Coverings of Regular Algebraic Maps
时间  Datetime
 
地点  Venue
报告人  Speaker
David Surowski (苏大卫) 教授
单位  Affiliation
Shanghai American School, Shanghai, and Kansas State University, Manhattan
邀请人  Host
吴耀坤
报告摘要  Abstract
One can think of an algebraic map as a natural combinatorial reinterpretation of a (usually compact) Riemann surface. As such, one would expect that some of the investigative tools used in the classical setting would not only have combinatorial counterparts, but that they would continue to be useful in the study of algebraic maps. One such tool is the combinatorial version of integral---or ``absolute"---homology. Emphasis is given the word absolute because a sufficiently general theory is needed to allow for the appearance of arbitrary abelian groups, especially those that appear as modules for other groups (viz., automorphism groups). What is to be exploited, then, are the resulting representation-theoretic aspects of the automorphism group G of an algebraic map M on abelian groups. We shall see that the extent to which such representations can be traced to coverings of the map M is largely controlled by the structure of the integral homology of M regarded as a G-module.