appliedtopology.wordpress.com

Applied Algebraic Topology

September 12, 2013. Speeding up Homology via Duality? In the last post. I constructed for any (locally finite) simplicial complex. A dual complex. Today, I thought of using this to gain a potential speed-up in computational homology. Note that simplicial homology of. Is the same as Cech homology of the cover given by open stars of the vertices of. This is because the nerve of this cover is precisely. And Cech homology is not-so-secretly the simplicial homology of the nerve. This presents a question of po...

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Applied Algebraic Topology | appliedtopology.wordpress.com Reviews

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September 12, 2013. Speeding up Homology via Duality? In the last post. I constructed for any (locally finite) simplicial complex. A dual complex. Today, I thought of using this to gain a potential speed-up in computational homology. Note that simplicial homology of. Is the same as Cech homology of the cover given by open stars of the vertices of. This is because the nerve of this cover is precisely. And Cech homology is not-so-secretly the simplicial homology of the nerve. This presents a question of po...

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Applied Algebraic Topology | appliedtopology.wordpress.com Reviews

https://appliedtopology.wordpress.com

September 12, 2013. Speeding up Homology via Duality? In the last post. I constructed for any (locally finite) simplicial complex. A dual complex. Today, I thought of using this to gain a potential speed-up in computational homology. Note that simplicial homology of. Is the same as Cech homology of the cover given by open stars of the vertices of. This is because the nerve of this cover is precisely. And Cech homology is not-so-secretly the simplicial homology of the nerve. This presents a question of po...

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appliedtopology.wordpress.com

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About | Applied Algebraic Topology

https://appliedtopology.wordpress.com/about

My name is Justin Curry and I am a PhD student at the University of Pennsylvania working with Robert Ghrist. My goal in this blog is to bring the latest developments in topological methods in applied mathematics to a wider audience. There should be something of interest here to mathematicians, computer scientists and engineers. Leave a Reply Cancel reply. Enter your comment here. Fill in your details below or click an icon to log in:. Address never made public). Notify me of new comments via email.

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Dual Simplicial Complexes | Applied Algebraic Topology

https://appliedtopology.wordpress.com/2013/09/11/dual-simplicial-complexes/comment-page-1

September 11, 2013. In the process of designing homework problems for Applied Algebraic Topology (ESE 680-003) last night, I stumbled upon a most beautiful application of the nerve theorem as well as a construction of a dual simplicial complex that is defined for any (locally finite) simplicial complex. This dual complex has the property that it is always homotopic to the original simplicial complex. Be a simplicial complex with vertex set. Is defined to be the set of simplices. To be the set of faces of.

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September | 2013 | Applied Algebraic Topology

https://appliedtopology.wordpress.com/2013/09

Monthly Archives: September 2013. September 12, 2013. Speeding up Homology via Duality? In the last post. I constructed for any (locally finite) simplicial complex. A dual complex. Today, I thought of using this to gain a potential speed-up in computational homology. Note that simplicial homology of. Is the same as Cech homology of the cover given by open stars of the vertices of. This is because the nerve of this cover is precisely. However, we know that the dual complex has the same homotopy type as.

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Learning AAT | Applied Algebraic Topology

https://appliedtopology.wordpress.com/learning-aat

There is a separate blog. Concerned with learning applied algebraic topology from the ground up. It is inspired by an on-going course that is being co-taught by myself (Justin Curry) and Robert Ghrist (my PhD advisor). Leave a Reply Cancel reply. Enter your comment here. Fill in your details below or click an icon to log in:. Address never made public). You are commenting using your WordPress.com account. ( Log Out. You are commenting using your Twitter account. ( Log Out. Speeding up Homology….

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Dual Simplicial Complexes | Applied Algebraic Topology

https://appliedtopology.wordpress.com/2013/09/11/dual-simplicial-complexes

September 11, 2013. In the process of designing homework problems for Applied Algebraic Topology (ESE 680-003) last night, I stumbled upon a most beautiful application of the nerve theorem as well as a construction of a dual simplicial complex that is defined for any (locally finite) simplicial complex. This dual complex has the property that it is always homotopic to the original simplicial complex. Be a simplicial complex with vertex set. Is defined to be the set of simplices. To be the set of faces of.

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Applied Algebraic Topology

September 12, 2013. Speeding up Homology via Duality? In the last post. I constructed for any (locally finite) simplicial complex. A dual complex. Today, I thought of using this to gain a potential speed-up in computational homology. Note that simplicial homology of. Is the same as Cech homology of the cover given by open stars of the vertices of. This is because the nerve of this cover is precisely. And Cech homology is not-so-secretly the simplicial homology of the nerve. This presents a question of po...

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