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This Week’s Finds
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Focus Session:
Jim delivered a talk on simplicial complexes with the primary goal of laying the groundwork for our upcoming discussion on homology. Key points from the talk included:
Introduction to Simplicial Complexes:
- Definitions and basic examples (vertices, edges, faces, etc.)
- How these discrete structures serve as combinatorial models for topological spaces
Motivation and Context:
- The role of simplicial complexes in bridging combinatorial topology and algebraic techniques
- An outline of how these ideas naturally lead into homology theory, setting the stage for further exploration in subsequent seminars
Discussion Points:
- Questions on the nuances of complex construction and the significance of simplicial maps
- Initial ideas on how to compute simplicial homology, emphasizing the transition from geometric intuition to algebraic formalism
Up Next:
Reading Group:
For next week’s reading we aim to be complete:
- Combination of readings for Homology
- Rotman, 3-5
- Hatcher, 1-2
- Lee Top, 5-6
References:
- Simplicial Complex: https://en.wikipedia.org/wiki/Simplicial_complex