The Challenge of Computing Homotopy Groups: Why Spheres Remain a Mystery - Sheena
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In the grand tapestry of mathematics, topology stands out for its unique approach to geometric shapes. It doesn't care about size or angles, but rather how spaces can be continuously deformed into one another, like stretching a clay model without tearing or gluing separate pieces. This seemingly abstract concept holds immense power, unlocking hidden properties of shapes and revealing a universe beyond our everyday perception of space.One of the central ideas in topology is the notion of a homotopy group. Imagine a loop drawn on a surface, like a circle on a sphere or a square on a plane.…mehr

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Produktbeschreibung
In the grand tapestry of mathematics, topology stands out for its unique approach to geometric shapes. It doesn't care about size or angles, but rather how spaces can be continuously deformed into one another, like stretching a clay model without tearing or gluing separate pieces. This seemingly abstract concept holds immense power, unlocking hidden properties of shapes and revealing a universe beyond our everyday perception of space.One of the central ideas in topology is the notion of a homotopy group. Imagine a loop drawn on a surface, like a circle on a sphere or a square on a plane. Homotopy groups classify these loops based on how they can be continuously deformed into one another without breaking the loop or letting it touch the edge of the surface. Intuitively, a loop that can be shrunk to a point without leaving the surface represents a "trivial" element in the group. More intricate loops that cannot be shrunk but can be continuously deformed into each other belong to the same class within the group.
Autorenporträt
Professor Sheena is a leading authority in the field of social media data analysis and its application to business strategy. Her pioneering research focuses on harnessing the power of platforms like Twitter to gain real-time insights into consumer behavior, brand perception, and market trends. Professor Sheena's expertise lies at the intersection of business resilience and disruption management. Through her work, she empowers organizations to navigate periods of significant change by leveraging the vast trove of information available on social media. In her book, "The Power of Tweets: Using Social Media Data to Understand Business Resilience in a Disrupted World," Professor Sheena equips readers with the tools and knowledge required to turn social media data into actionable intelligence. This vital resource empowers businesses to not only weather disruption but also emerge stronger and more adaptable. Professor Sheena's extensive experience extends beyond academia. She is a sought-after consultant who has partnered with numerous Fortune 500 companies, helping them develop data-driven strategies for success in today's dynamic business landscape.