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The loop orbifold of the symmetric product

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Ernesto Lupercio, Bernardo Uribe, Miguel A. Xicoténcatl

Algebraic Topology · Submitted 22 Jun 2006

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim By using the loop orbifold of the symmetric product, we give a formula for the Poincar\'e polynomial of the free loop space of the Borel construction of the symmetric product.

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arXiv IDmath/0606573 (version 1)
Pith IDTP3N4URY, Pith's permanent record of this paper and its review
CitationBernardo Uribe, Ernesto Lupercio, Miguel A. Xicot\'encatl. "The loop orbifold of the symmetric product." arXiv:math/0606573 (2006). https://pith.science/paper/TP3N4URY
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,009 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.15 · compares with prior results 0.93 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

By using the loop orbifold of the symmetric product, we give a formula for the Poincar\'e polynomial of the free loop space of the Borel construction of the symmetric product. We also show that the Chas-Sullivan product structure in the homology of the free loop space of the Borel construction of the symmetric product induces a ring structure in the homology of the inertia orbifold of the symmetric product. This ring structure is compared to the one in cohomology defined through the usual field theory formalism as in the theory of Chen and Ruan.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 By using the loop orbifold of the symmetric product, we give a formula for the Poincar\'e polynomial of the free loop space of the Borel construction of the symmetric product. result 0.64 0.95 0.62 asserted 1.00
s1 We also show that the Chas-Sullivan product structure in the homology of the free loop space of the Borel construction of the symmetric product induces a ring structure in the homology of the inertia orbifold of the symmetric product. result 0.94 0.95 0.31 asserted 1.00
s2 This ring structure is compared to the one in cohomology defined through the usual field theory formalism as in the theory of Chen and Ruan. contribution 0.42 0.74 0.14 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

By using the loop orbifold of the symmetric product, we give a formula for the Poincar\'e polynomial of the free loop space of the Borel construction of the symmetric product. We also show that the Chas-Sullivan product structure in the homology of the free loop space of the Borel construction of the symmetric product induces a ring structure in the homology of the inertia orbifold of the symmetric product. This ring structure is compared to the one in cohomology defined through the usual field theory formalism as in the theory of Chen and Ruan.

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